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Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8650

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Citation - WoS: 69
Citation - Scopus: 90
Analysis of Fractional Model of Guava for Biological Pest Control With Memory Effect
(Elsevier, 2021) Ganbari, Behzad; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
Introduction: Fractional operators find their applications in several scientific and engineering processes. We consider a fractional guava fruit model involving a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. The fractional guava fruit model is considered as a Lotka-Volterra nature. Objectives: The main objective of this work is to study a guava fruit model associated with a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. Methods: Existence and uniqueness analysis of the solution is evaluated effectively by using Picard Lindelof approach. An approximate numerical solution of the fractional guava fruit problem is obtained via a numerical scheme. Results: The positivity analysis and equilibrium analysis for the fractional guava fruit model is discussed. The numerical results are demonstrated to prove our theoretical results. The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters is discussed. Conclusion: The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters shows new vista and interesting phenomena of the model. The results are indicating that the fractional approach with non-singular kernel plays an important role in the study of different scientific problems. The suggested numerical scheme is very efficient for solving nonlinear fractional models of physical importance. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 64
Citation - Scopus: 63
Comparative Study of Artificial Neural Network Versus Parametric Method in Covid-19 Data Analysis
(Elsevier, 2022) Colak, Andac Batur; Sindhu, Tabassum Naz; Lone, Showkat Ahmad; Alsubie, Abdelaziz; Jarad, Fahd; Shafiq, Anum
Since the previous two years, a new coronavirus (COVID-19) has found a major global problem. The speedy pathogen over the globe was followed by a shockingly large number of afflicted people and a gradual increase in the number of deaths. If the survival analysis of active individuals can be predicted, it will help to contain the epidemic significantly in any area. In medical diagnosis, prognosis and survival analysis, neural networks have been found to be as successful as general nonlinear models. In this study, a real application has been developed for estimating the COVID-19 mortality rates in Italy by using two different methods, artificial neural network modeling and maximum likelihood estimation. The predictions obtained from the multilayer artificial neural network model developed with 9 neurons in the hidden layer were compared with the numerical results. The maximum deviation calculated for the artificial neural network model was -0.14% and the R value was 0.99836. The study findings confirmed that the two different statistical models that were developed had high reliability.
Citation - WoS: 49
Citation - Scopus: 55
Continuous Wavelet and Derivative Transforms for the Simultaneous Quantitative Analysis and Dissolution Test of Levodopa-Benserazide Tablets
(Elsevier, 2007) Kaya, Sueha; Doganay, Tanver; Baleanu, Dumitru; Dinc, Erdal
Simultaneous analyses and dissolution tests of levodopa-benserazide tablets were carried out by continuous wavelet transform (CWT) and classic derivative spectrophotometry (DS) without using any chemical separation step. The developed two spectrophotometric resolutions are based on the transformation of the original UV spectra. The original absorption spectra of levodopa and benserazide in the concentration range of 1-80 mu g/mL and 5-240 mu g/mL in USP simulated gastric juice were registered in the spectral range of 250-310 nm, respectively. Various wavelet families and different spectrophotometric derivative orders were tested to find the optimal signal processing for obtaining desirable calibration graphs and reliable determinations of the investigated drugs. Under the optimized conditions of the methods, symlets wavelet family using a = 128 with sixth order (SYM6-CWT) and the first derivative transform with Delta lambda = 10 nm were identified as optimal signal processing methods for the determinations and dissolution tests. The calibration functions for each drug were obtained by measuring the values of the CWT and derivative amplitudes. The validation of the developed methods was confirmed by analyzing various synthetic mixtures of the investigated drugs. Mean recovery values were found between 99.1% and 104.7% for DS and 100% and 102.9% for CWT, respectively for determination of BEN and LEV in synthetic mixtures. Each developed approaches were successfully applied to the simultaneous determination and dissolution test of levodopa and benserazide in their commercial tablets and a good agreement was observed. (c) 2007 Elsevier B.V. All rights reserved.
Citation - WoS: 72
Citation - Scopus: 78
Dynamical Behaviours and Stability Analysis of a Generalized Fractional Model With a Real Case Study
(Elsevier, 2023) Baleanu, D.; Arshad, S.; Jajarmi, A.; Shokat, W.; Ghassabzade, F. Akhavan; Wali, M.
Introduction: Mathematical modelling is a rapidly expanding field that offers new and interesting oppor-tunities for both mathematicians and biologists. Concerning COVID-19, this powerful tool may help humans to prevent the spread of this disease, which has affected the livelihood of all people badly. Objectives: The main objective of this research is to explore an efficient mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework.Methods: The new model in this paper is formulated in the Caputo sense, employs a nonlinear time -varying transmission rate, and consists of ten population classes including susceptible, infected, diag-nosed, ailing, recognized, infected real, threatened, diagnosed recovered, healed, and extinct people. The existence of a unique solution is explored for the new model, and the associated dynamical beha-viours are discussed in terms of equilibrium points, invariant region, local and global stability, and basic reproduction number. To implement the proposed model numerically, an efficient approximation scheme is employed by the combination of Laplace transform and a successive substitution approach; besides, the corresponding convergence analysis is also investigated.Results: Numerical simulations are reported for various fractional orders, and simulation results are com-pared with a real case of COVID-19 pandemic in Italy. By using these comparisons between the simulated and measured data, we find the best value of the fractional order with minimum absolute and relative errors. Also, the impact of different parameters on the spread of viral infection is analyzed and studied.Conclusion: According to the comparative results with real data, we justify the use of fractional concepts in the mathematical modelling, for the new non-integer formalism simulates the reality more precisely than the classical framework.& COPY; 2023 The Authors. Published by Elsevier B.V. on behalf of Cairo University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Citation - WoS: 2
Citation - Scopus: 3
Editorial Note on the Special Issue: "fractional Calculus Models for the Dynamics of Complex Systems
(Elsevier, 2021) Kumar, Devendra; Pinto, Carla M. A.; Baleanu, Dumitru; Sweilam, Nasser H.
Citation - WoS: 12
Citation - Scopus: 16
Fast Fluorometric Enumeration of E. Coli Using Passive Chip
(Elsevier, 2019) Cogun, Ferah; Yildirim, Ender; Boyaci, Ismail Haklu; Cetin, Demet; Ertas, Nusret; Kasap, Esin Nagihan; Dogan, Uzeyir
In this report, a passive microfluidic chip design was developed for fast and sensitive fluorometric determination of Escherichia coli (E. coli) based on sandwich immunoassay. Initially, magnetic nanoparticles (MNPs) and chitosan modified mercaptopropionic acid capped cadmium telluride (CdTe) quantum dots (QDs) were functionalized with E.coli specific antibody to form a sandwich immunoassay with the E. coli. The magnetic separation and preconcentration of the E.coli from the sample solution was performed in the vial. Conjugation of QDs to the magnetically captured E. coli and washing were performed using a passive type of microchip. The microfluidic chip consists of four microchambers connected to each other by microchannels which act as capillary valves. Signal measurement was performed at the last chamber by using a hand-held spectrofluorometer equipped with a fiber optic reflection probe. The selectivity of the method was tested with Enterobacter aerogenes (E. aerogenes) and Salmonella enteritidis (S. enteritidis), it was observed that these bacteria have no interference effect on E.coli determination. The calibration curve was found to be linear in the range of 10(1)-10(5) cfu/mL with a correlation coefficient higher than 0.99. The limit of detection was calculated as 5 cfu/mL. The method was successfully applied to spiked tap and lake water samples. The results suggest that the developed method is applicable for on-site E. coli detection and offers several advantages such as large dynamic range, high sensitivity, high selectivity and short analysis time.
Citation - WoS: 32
Citation - Scopus: 39
Finite-Time Stabilization of a Perturbed Chaotic Finance Model
(Elsevier, 2021) Ouannas, Adel; Shafiq, Muhammad; Pham, Viet-Thanh; Baleanu, Dumitru; Ahmad, Israr
Introduction: Robust, stable financial systems significantly improve the growth of an economic system. The stabilization of financial systems poses the following challenges. The state variables' trajectories (i) lie outside the basin of attraction, (ii) have high oscillations, and (iii) converge to the equilibrium state slowly. Objectives: This paper aims to design a controller that develops a robust, stable financial closed-loop system to address the challenges above by (i) attracting all state variables to the origin, (ii) reducing the oscillations, and (iii) increasing the gradient of the convergence. Methods: This paper proposes a detailed mathematical analysis of the steady-state stability, dissipative characteristics, the Lyapunov exponents, bifurcation phenomena, and Poincare maps of chaotic financial dynamic systems. The proposed controller does not cancel the nonlinear terms appearing in the closed-loop. This structure is robust to the smoothly varying system parameters and improves closedloop efficiency. Further, the controller eradicates the effects of inevitable exogenous disturbances and accomplishes a faster, oscillation-free convergence of the perturbed state variables to the desired steady-state within a finite time. The Lyapunov stability analysis proves the closed-loop global stability. The paper also discusses finite-time stability analysis and describes the controller parameters' effects on the convergence rates. Computer-based simulations endorse the theoretical findings, and the comparative study highlights the benefits. Results: Theoretical analysis proofs and computer simulation results verify that the proposed controller compels the state trajectories, including trajectories outside the basin of attraction, to the origin within finite time without oscillations while being faster than the other controllers discussed in the comparative study section. Conclusions: This article proposes a novel robust, nonlinear finite-time controller for the robust stabilization of the chaotic finance model. It provides an in-depth analysis based on the Lyapunov stability theory and computer simulation results to verify the robust convergence of the state variables to the origin. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 38
Citation - Scopus: 38
A Hybrid Fractional Optimal Control for a Novel Coronavirus (2019-Ncov) Mathematical Model
(Elsevier, 2021) AL-Mekhlafi, S. M.; Baleanu, D.; Sweilam, N. H.
Introduction: Coronavirus COVID-19 pandemic is the defining global health crisis of our time and the greatest challenge we have faced since world war two. To describe this disease mathematically, we noted that COVID-19, due to uncertainties associated to the pandemic, ordinal derivatives and their associated integral operators show deficient. The fractional order differential equations models seem more consistent with this disease than the integer order models. This is due to the fact that fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes. Hence there is a growing need to study and use the fractional order differential equations. Also, optimal control theory is very important topic to control the variables in mathematical models of infectious disease. Moreover, a hybrid fractional operator which may be expressed as a linear combination of the Caputo fractional derivative and the Riemann-Liouville fractional integral is recently introduced. This new operator is more general than the operator of Caputo's fractional derivative. Numerical techniques are very important tool in this area of research because most fractional order problems do not have exact analytic solutions. Objectives: A novel fractional order Coronavirus (2019-nCov) mathematical model with modified parameters will be presented. Optimal control of the suggested model is the main objective of this work. Three control variables are presented in this model to minimize the number of infected populations. Necessary control conditions will be derived. Methods: The numerical methods used to study the fractional optimality system are the weighted average nonstandard finite difference method and the Grunwald-Letnikov nonstandard finite difference method. Results: The proposed model with a new fractional operator is presented. We have successfully applied a kind of Pontryagin's maximum principle and were able to reduce the number of infected people using the proposed numerical methods. The weighted average nonstandard finite difference method with the new operator derivative has the best results than Grunwald-Letnikov nonstandard finite difference method with the same operator. Moreover, the proposed methods with the new operator have the best results than the proposed methods with Caputo operator. Conclusions: The combination of fractional order derivative and optimal control in the Coronavirus (2019-nCov) mathematical model improves the dynamics of the model. The new operator is more general and suitable to study the optimal control of the proposed model than the Caputo operator and could be more useful for the researchers and scientists. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 2
Citation - Scopus: 3
The Investigation of Energy Management and Atomic Interaction Between Coronavirus Structure in the Vicinity of Aqueous Environment of H2o Molecules Via Molecular Dynamics Approach
(Elsevier, 2021) Bajuri, Mohd Yazid; Alrabaiah, Hussam; Muhammad, Taseer; Sajadi, S. Mohammad; Ghaemi, Ferial; Karimipour, Arash; Guo, Hui-Hui
The coronavirus pandemic is caused by intense acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Identifying the atomic structure of this virus can lead to the treatment of related diseases in medical cases. In the current computational study, the atomic evolution of the coronavirus in an aqueous environment using the Molecular Dynamics (MD) approach is explained. The virus behaviors by reporting the physical attributes such as total energy, temperature, potential energy, interaction energy, volume, entropy, and radius of gyration of the modeled virus are reported. The MD results indicated the atomic stability of the simulated virus significantly reduced after 25.33 ns. Furthermore, the volume of simulated virus changes from 182397 angstrom(3) to 372589 angstrom(3) after t = 30 ns. This result shows the atomic interaction between various atoms in coronavirus structure decreases in the vicinity of H2O molecules. Numerically, the interaction energy between virus and aqueous environment converges to -12387 eV and -251 eV values in the initial and final time steps of the MD study procedure, respectively. (C) 2021 Elsevier B.V. All rights reserved.
Citation - WoS: 33
Citation - Scopus: 35
Mathematical Analysis for the Effect of Voluntary Vaccination on the Propagation of Corona Virus Pandemic
(Elsevier, 2021) Abbas, M.; Rafiq, M.; Baleanu, D.; Ahmad, W.
In this manuscript, a new nonlinear model for the rapidly spreading Corona virus disease (COVID-19) is developed. We incorporate an additional class of vaccinated humans which ascertains the impact of vaccination strategy for susceptible humans. A complete mathematical analysis of this model is conducted to predict the dynamics of Corona virus in the population. The analysis proves the effectiveness of vaccination strategy employed and helps public health services to control or to reduce the burden of corona virus pandemic. We first prove the existence and uniqueness and then boundedness and positivity of solutions. Threshold parameter for the vaccination model is computed analytically. Stability of the proposed model at fixed points is investigated analytically with the help of threshold parameter to examine epidemiological relevance of the pandemic. We apply LaSalle's invariance principle from the theory of Lyapunov function to prove the global stability of both the equilibria. Two well known numerical techniques namely Runge-Kutta method of order 4 (RK4), and the Non-Standard Finite Difference (NSFD) method are employed to solve the system of ODE's and to validate our obtained theoretical results. For different coverage levels of voluntary vaccination, we explored a complete quantitative analysis of the model. To draw our conclusions, the effect of proposed vaccination on threshold parameter is studied numerically. It is claimed that Corona virus disease could be eradicated faster if a human community selfishly adopts mandatory vaccination measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effect of vaccination strategy on a disease dynamics.
Citation - WoS: 17
Citation - Scopus: 21
Mathematical Modeling and Analysis of the Novel Coronavirus Using Atangana-Baleanu Derivative
(Elsevier, 2021) El-Dessoky, M. M.; Baleanu, Dumitru; Alzahrani, Ebraheem
The novel Coronavirus infection disease is becoming more complex for the humans society by giving death and infected cases throughout the world. Due to this infection, many countries of the world suffers from great economic loss. The researchers around the world are very active to make a plan and policy for its early eradication. The government officials have taken full action for the eradication of this virus using different possible control strategies. It is the first priority of the researchers to develop safe vaccine against this deadly disease to minimize the infection. Different approaches have been made in this regards for its elimination. In this study, we formulate a mathematical epidemic model to analyze the dynamical behavior and transmission patterns of this new pandemic. We consider the environmental viral concentration in the model to better study the disease incidence in a community. Initially, the model is constructed with the derivative of integer order. The classical epidemic model is then reconstructed with the fractional order operator in the form of Atangana-Baleanu derivative with the nonsingular and nonlocal kernel in order to analyze the dynamics of Coronavirus infection in a better way. A well-known estimation approach is used to estimate model parameters from the COVID-19 cases reported in Saudi Arabia from March 1 till August 20, 2020. After the procedure of parameters estimation, we explore some basic mathematical analysis of the fractional model. The stability results are provided for the disease free case using fractional stability concepts. Further, the uniqueness and existence results will be shown using the Picard-Lendelof approach. Moreover, an efficient numerical scheme has been proposed to obtain the solution of the model numerically. Finally, using the real fitted parameters, we depict many simulation results in order to demonstrate the importance of various model parameters and the memory index on disease dynamics and possible eradication.
Citation - WoS: 6
Citation - Scopus: 6
Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage
(Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, Thabet
Middle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.
Citation - WoS: 37
Citation - Scopus: 43
Multivariate Analysis of Paracetamol, Propiphenazone, Caffeine and Thiamine in Quaternary Mixtures by Pcr, Pls and Ann Calibrations Applied on Wavelet Transform Data
(Elsevier, 2008) Baleanu, Dumitru; Ioele, Giuseppina; De Luca, Michele; Ragno, Gaetano; Dinc, Erdal
The quantitative resolution of a quaternary pharmaceutical mixture consisting of paracetamol, propiphenazone, caffeine and thiamine was performed by the simultaneous use of fractional wavelet transform (FWT) with principal component regression (PCR), partial least squares (PLS) and artificial neural networks (ANN) methods. A calibration set consisting of 22 mixture solutions was prepared by means of an orthogonal experimental design and their absorption spectra were recorded in the spectral range of 210.0-312.3 nm and then transferred into the fractional wavelet domain and processed by FWT. The chemometric calibrations FWT-PCR, FWT-PLS and FWT-ANN were computed by using the relationship between the coefficients provided by FWT method and the concentration data from calibration set. An external validation was carried out by applying the developed methods to the analysis of synthetic mixtures of the related compounds, obtaining successful results. The models were finally used to assay the studied drugs in the commercial pharmaceutical formulations. (c) 2008 Elsevier B.V. All rights reserved.
Citation - WoS: 28
Citation - Scopus: 32
New Applications Related To Covid-19
(Elsevier, 2021) Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur; Akgul, Ali
Analysis of mathematical models projected for COVID-19 presents in many valuable outputs. We analyze a model of differential equation related to Covid-19 in this paper. We use fractal-fractional derivatives in the proposed model. We analyze the equilibria of the model. We discuss the stability analysis in details. We apply very effective method to obtain the numerical results. We demonstrate our results by the numerical simulations.
Citation - WoS: 17
Citation - Scopus: 21
Nonstandard Finite Difference Method for Solving Complex-Order Fractional Burgers' Equations
(Elsevier, 2020) AL-Mekhlafi, S. M.; Baleanu, D.; Sweilam, N. H.
The aim of this work is to present numerical treatments to a complex order fractional nonlinear one-dimensional problem of Burgers' equations. A new parameter sigma(t) is presented in order to be consistent with the physical model problem. This parameter characterizes the existence of fractional structures in the equations. A relation between the parameter sigma(t) and the time derivative complex order is derived. An unconditionally stable numerical scheme using a kind of weighted average nonstandard finite-difference discretization is presented. Stability analysis of this method is studied. Numerical simulations are given to confirm the reliability of the proposed method. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 4
Citation - Scopus: 6
Numerical Treatments for the Optimal Control of Two Types Variable-Order Covid-19 Model
(Elsevier, 2022) Al-Mekhlafi, Seham; Shatta, Salma; Baleanu, Dumitru; Sweilam, Nasser
In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable -order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge-Kutta method and the non-standard generalized fifth-order Runge-Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies' simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.
Citation - WoS: 44
Citation - Scopus: 53
On a New Conceptual Mathematical Model Dealing the Current Novel Coronavirus-19 Infectious Disease
(Elsevier, 2020) Shah, Kamal; Seadawy, Aly; Alrabaiah, Hussam; Baleanu, Dumitru; Din, Anwarud
The present paper describes a three compartment mathematical model to study the transmission of the current infection due to the novel coronavirus (2019-nCoV or COVID-19). We investigate the aforesaid dynamical model by using Atangana, Baleanu and Caputo (ABC) derivative with arbitrary order. We derive some existence results together with stability of Hyers-Ulam type. Further for numerical simulations, we use Adams-Bashforth (AB) method with fractional differentiation. The mentioned method is a powerful tool to investigate nonlinear problems for their respective simulation. Some discussion and future remarks are also given.
Citation - WoS: 9
Citation - Scopus: 13
Orthonormal Piecewise Vieta-Lucas Functions for the Numerical Solution of the One- and Two-Dimensional Piecewise Fractional Galilei Invariant Advection-Diffusion Equations
(Elsevier, 2023) Razzaghi, Mohsen; Baleanu, Dumitru; Heydari, Mohammad Hossein
Introduction: Recently, a new family of fractional derivatives called the piecewise fractional derivatives has been introduced, arguing that for some problems, each of the classical fractional derivatives may not be able to provide an accurate statement of the consideration problem alone. In defining this kind of derivatives, several types of fractional derivatives can be used simultaneously. Objectives: This study introduces a new kind of piecewise fractional derivative by employing the Caputo type distributed-order fractional derivative and ABC fractional derivative. The one-and two-dimensional piecewise fractional Galilei invariant advection-diffusion equations are defined using this piecewise frac-tional derivative.Methods: A new class of basis functions called the orthonormal piecewise Vieta-Lucas (VL) functions are defined. Fractional derivatives of these functions in the Caputo and ABC senses are computed. These func-tions are utilized to construct two numerical methods for solving the introduced problems under non -local boundary conditions. The proposed methods convert solving the original problems into solving sys-tems of algebraic equations. Results: The accuracy and convergence order of the proposed methods are examined by solving several examples. The obtained results are investigated, numerically.Conclusion: This study introduces a kind of piecewise fractional derivative. This derivative is employed to define the one-and two-dimensional piecewise fractional Galilei invariant advection-diffusion equa-tions. Two numerical methods based on the orthonormal VL polynomials and orthonormal piecewise VL functions are established for these problems. The numerical results obtained from solving several examples confirm the high accuracy of the proposed methods.& COPY; 2022 The Authors. Published by Elsevier B.V. on behalf of Cairo University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Citation - WoS: 5
Citation - Scopus: 8
Predictive Dynamical Modeling and Stability of the Equilibria in a Discrete Fractional Difference Covid-19 Epidemic Model
(Elsevier, 2023) Rashid, Saima; Akdemir, Ahmet Ocak; Khalid, Aasma; Baleanu, Dumitru; Al-Sinan, Bushra R.; Elzibar, O. A. I.; Chu, Yu-Ming
The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R0. Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelof technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.
Citation - WoS: 36
Citation - Scopus: 43
Stable Numerical Results To a Class of Time-Space Fractional Partial Differential Equations Via Spectral Method
(Elsevier, 2020) Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd
In this paper, we are concerned with finding numerical solutions to the class of time-space fractional partial differential equations: D(t)(p)u(t, x) + kappa D(x)(p)u(t, x) + tau u(t, x) = g(t, x), 1 < p < 2, (t, x) is an element of [0,1] x [0, 1], under the initial conditions. u(0, x) = theta(x), u(t)(0, x) = phi(x), and the mixed boundary conditions. u(t, 0) = u(x)(t, 0) = 0, where D-t(p) is the arbitrary derivative in Caputo sense of order p corresponding to the variable time t. Further, D-x(p) is the arbitrary derivative in Caputo sense with order p corresponding to the variable space x. Using shifted Jacobin polynomial basis and via some operational matrices of fractional order integration and differentiation, the considered problem is reduced to solve a system of linear equations. The used method doesn't need discretization. A test problem is presented in order to validate the method. Moreover, it is shown by some numerical tests that the suggested method is stable with respect to a small perturbation of the source data g(t, x). Further the exact and numerical solutions are compared via 3D graphs which shows that both the solutions coincides very well. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.

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