Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 6Citation - Scopus: 6Modeling 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, ThabetMiddle 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.Article Citation - WoS: 1Citation - Scopus: 2Testing the Equality of Several Independent Stationary and Non-Stationary Time Series Models with Fractional Brownian Motion Errors(Elsevier, 2021) Mahmoudi, Mohammad Reza; Baleanu, Dumitru; Qasem, Sultan Noman; Mosavi, Amirhosein; Band, Shahab S.; S. Band, ShahabThis work is devoted to apply the parametric and nonparametric techniques to construct test of hypothesis about the equality of the probabilistic behaviors of several time series models with fractional Brownian motion errors fitted on several independent datasets. The accuracy and power of the introduced method are studied using the simulated and real datasets. The results indicate that the introduced approach is more powerful than other alternative approaches, in non-stationary cases. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Article Citation - WoS: 1Citation - Scopus: 2On the Complementary Nabla Pachpatte Type Dynamic Inequalities Via Convexity(Elsevier, 2024) Kaymakcalan, Billur; Kayar, ZeynepPachpatte type inequalities are convex generalizations of the well-known Hardy-Copson type inequalities. As Hardy-Copson type inequalities and convexity have numerous applications in pure and applied mathematics, combining these concepts will lead to more significant applications that can be used to develop certain branches of mathematics such as fuctional analysis, operator theory, optimization and ordinary/partial differential equations. We extend classical nabla Pachpatte type dynamic inequalities by changing the interval of the exponent delta from delta > 1 to delta < 0. Our results not only complement the classical nabla Pachpatte type inequalities but also generalize complementary nabla Hardy-Copson type inequalities. As the case of delta < 0 has not been previously examined, these complementary inequalities represent a novelty in the nabla time scale calculus, specialized cases in continuous and discrete scenarios, and in the dual outcomes derived in the delta time scale calculus.Article Citation - WoS: 10Citation - Scopus: 11New Insights for the Fuzzy Fractional Partial Differential Equations Pertaining To Katugampola Generalized Hukuhara Differentiability in the Frame of Caputo Operator and Fixed Point Technique(Elsevier, 2024) Jarad, Fahd; Alamri, Hind; Rashid, SaimaIn this article, we use the Caputo-Katugampola gH-differentiability to solve a class of fractional PDE systems. With the aid of Caputo-Katugampola gH-differentiability, we demonstrate the existence and uniqueness outcomes of two types of gH-weak findings of the framework of fuzzy fractional coupled PDEs using Lipschitz assumptions and employing the Banach fixed point theorem with the mathematical induction technique. Moreover, owing to the entanglement in the initial value problems (IVPs), we establish the p Gronwall inequality of the matrix pattern and inventively explain the continuous dependence of the coupled framework's responses on the given assumptions and the epsilon-approximate solution of the coupled system. An illustrative example is provided to demonstrate that their existence and unique outcomes are accurate. Through experimentation, we demonstrate the efficacy of the suggested approach in resolving fractional differential equation algorithms under conditions of uncertainty found in engineering and physical phenomena. Additionally, comparisons are drawn for the computed outcomes. Ultimately, we make several suggestions for futuristic work.Article Citation - WoS: 35Citation - Scopus: 38Heat Transfer Analysis of Magnetized Cu-Ag Hybrid Nanofluid Radiative Flow Over a Spinning Disk When the Exponential Heat Source and Hall Current Are Substantial: Optimization and Sensitivity Analysis(Elsevier, 2023) Pyari, Devarsu Radha; Ontela, Surender; Al-Mdallal, Qasem M.; Jarad, Fahd; Thumma, ThirupathiThe main motive of the instigated mathematical model is to observe the impact of Hall current on the hybrid nanofluid flow over a disk that is rotating. The copper and silver metal nanoparticles have been considered with volume fraction phi 1 = phi 2 = 0.01(0.01)0.04 and are suspended in water to form the hybrid nanofluid. Diverse characteristics like magnetic field, thermal radiation, and (ESHS) exponential space dependent heat source are incorporated to investigate the nature of the flow. The present mathematical model is initiated with partial derivative equations (PDEs) which are redrafted as ordinary derivative equations (ODEs) with appropriate transformations of similarity. The results are attained through a blend of the Runge-Kutta method, shooting procedure, and the influences of parameters on the flow of nanofluid and hybrid nanofluid are compared and illustrated both as tables and graphs. The present numerical research is unique because by employing a complete quadratic CCD framework using the RSM strategy, the sensitivity and optimization analysis of the heat transmission improvement for the volume fraction, ESHS, and thermal radiation parameters have been performed. The R-squared and adjusted R-Squared are obtained as 100%. The residual graphs and contour diagrams of the same are also shown. The current study establishes that the Hall parameter increases the radial velocity, but it also controls the energy and cross-radial velocity. The rate of heat transmission is increased by thermal radiation even at low levels of ESHS. The rate of heat transmission is more sensitive (0.024670) to the volume fraction of the hybrid nanofluid when ESHS is at an intermediate level. The lowest sensitivity (-1.269967) value towards ESHS is observed For thermal radiation and ESHS parameter values, the heat transmission rate of the mono nanofluid is not as great as that of hybridArticle Citation - WoS: 26Citation - Scopus: 31Analysis of Mixed Type Nonlinear Volterra-Fredholm Integral Equations Involving the Erdelyi-Kober Fractional Operator(Elsevier, 2023) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Paul, Supriya KumarThis paper investigates the existence, uniqueness and stability of solutions to the nonlinear Volterra-Fredholm integral equations (NVFIE) involving the Erdelyi-Kober (E-K) fractional integral operator. We use the Leray- Schauder alternative and Banach's fixed point theorem to examine the existence and uniqueness of solutions, and we also explore Hyers-Ulam (H-U) and Hyers-Ulam-Rassias (H-U-R) stability in the space C([0, fl], R). Furthermore, three solution sets U-sigma,U-lambda, U-theta,U-1 and U-1,U-1 are constructed for sigma > 0, lambda > 0, and theta is an element of (0,1), and then we obtain local stability of the solutions with some ideal conditions and by using Schauder fixed point theorem on these three sets, respectively. Also, to achieve the goal, we choose the parameters for the NVFIE as delta is an element of (1/2, 1), p is an element of (0,1), gamma > 0. Three examples are provided to clarify the results.Article Citation - WoS: 13Citation - Scopus: 15Some Estimation Methods for Mixture of Extreme Value Distributions With Simulation and Application in Medicine(Elsevier, 2022) Anwar, Sadia; Sindhu, Tabassum Naz; Jarad, Fahd; Lone, Showkat AhmadIn recent years, statisticians have grown increasingly engaged in research of mixture models, particularly in the previous decade, without adequate consideration of challenge of estimating the parameters of mixture models from a frequentist perspective. Except for maximum likelihood estimation, this study addresses this vacuum by discussing the two other classical methods of estimation for mixture model. We commence by briefly describing the three frequentist approaches, namely maximum likelihood, ordinary, and weighted least squares, and then comparing them through extensive numerical simulations. The model's applicability is illustrated by its application to simulated and real-world data, which yields promising results in terms of enhanced estimation.Article Citation - WoS: 18Citation - Scopus: 18Profit and Efficiency Enhancement of a Cylindrical Solar Collector by Structural Modification of Helical Tube(Elsevier, 2022) Mansir, Ibrahim B.; Sharma, Kamal; Mahariq, Ibrahim; Jarad, Fahd; Youshanlouei, Mohammad Mehdizadeh; Reda, Shaker A.; Luo, JieCylindrical solar collectors (CSCs) are getting attraction. Heat extraction part of these instruments consists of a helical tube which transfers thermal energy to working fluid. Enhancement of the heat transfer process within this part leads to enhancement of energy achievement. In this paper, influence of applying helical corrugation on helical absorber was evaluated. The number of corrugations and pitch and height of corrugations were considered as variant parameters. The system was evaluated from different viewpoints and performance of system was analyzed based on performance factor and economic viewpoints. The results revealed that the presence of helical Corrugation could increase heat transfer up to 19%. It was found that Dean number of 3000 could be considered as a critical Dean number from view point of performance factor. The application of the proposed system was more beneficial at Dean numbers below 3000. It was revealed that the application of helical corrugation could provide up to 24% enhancement in economic advantage of the system. Best economic performance was related to case with four starts which had corrugation height and corrugation pitch of 0.002 m and 0.103 m and occurred at Dean number of 2000.Article Citation - WoS: 23Citation - Scopus: 23Performance Boost of a Helical Heat Absorber by Utilization of Twisted Tape Turbulator, an Experimental Investigation(Elsevier, 2022) Xie, Changgui; Mansir, Ibrahim B.; Mahariq, Ibrahim; Singh, Pradeep Kumar; Arsalanloo, Akbar; Shahzad, Rehman Muhammad; Jarad, FahdPresent investigation, experimentally probes the influence of utilization of twisted tape turbulator inside a helical tube. Twisted tapes mix the flow and enhance the heat transfer rate. The pitch of twisted tape was considered as variant parameter. Tube was considered to be under constant heat flux. Also, Re number was within the range of 6000-32000 which denotes that flow was the turbulent flow regime. Various parameters including Nu number, friction factor and entropy generation were evaluated. Furthermore, performance evaluation criteria based on first law and second law of thermodynamics together with economic performance parameters were evaluated. The results revealed that by the increment of water flow rate and the decrement of twist pitch the Nu number would face a rise of 66% in comparison with the smooth helical tube. Also, it was found that the application of twisted tape has more effect on frictional entropy generation rather than thermal entropy generation. Finally, the results indicated that the maximum value of eta(c) was about 1.59 x 10(-7) ($/J) which presented up to 2.7 times enhancing in the financial beneficial of the helical tube.Article Citation - WoS: 9Citation - Scopus: 13Orthonormal 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 HosseinIntroduction: 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/).