PubMed İndeksli Yayınlar Koleksiyonu

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

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Now showing 1 - 19 of 19

Citation - WoS: 26
Citation - Scopus: 31
Asymptotic Solutions of Fractional Interval Differential Equations With Nonsingular Kernel Derivative
(Amer inst Physics, 2019) Ahmadian, A.; Salimi, M.; Ferrara, M.; Baleanu, D.; Salahshour, S.
Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters. Published under license by AIP Publishing.
Citation - WoS: 33
Citation - Scopus: 39
Design of a Fractional-Order Atmospheric Model Via a Class of Act-Like Chaotic System and Its Sliding Mode Chaos Control
(Aip Publishing, 2023) Baishya, Chandrali; Veeresha, Pundikala; Baleanu, Dumitru; Naik, Manisha Krishna
Investigation of the dynamical behavior related to environmental phenomena has received much attention across a variety of scientific domains. One such phenomenon is global warming. The main causes of global warming, which has detrimental effects on our ecosystem, are mainly excess greenhouse gases and temperature. Looking at the significance of this climatic event, in this study, we have connected the ACT-like model to three climatic components, namely, permafrost thaw, temperature, and greenhouse gases in the form of a Caputo fractional differential equation, and analyzed their dynamics. The theoretical aspects, such as the existence and uniqueness of the obtained solution, are examined. We have derived two different sliding mode controllers to control chaos in this fractional-order system. The influences of these controllers are analyzed in the presence of uncertainties and external disturbances. In this process, we have obtained a new controlled system of equations without and with uncertainties and external disturbances. Global stability of these new systems is also established. All the aspects are examined for commensurate and non-commensurate fractional-order derivatives. To establish that the system is chaotic, we have taken the assistance of the Lyapunov exponent and the bifurcation diagram with respect to the fractional derivative. To perform numerical simulation, we have identified certain values of the parameters where the system exhibits chaotic behavior. Then, the theoretical claims about the influence of the controller on the system are established with the help of numerical simulations.
Citation - WoS: 2
Existence of Measure Pseudo-Almost Automorphic Functions and Applications To Impulsive Integro-Differential Equation
(Aip Publishing, 2021) Baleanu, Dumitru; George, Soumya; Grayna, J.; Kavitha, V.
This article's main objective is to establish the measure pseudo-almost automorphic solution of an integro-differential equation with impulses. We develop the existence results based on the Banach contraction principle mapping and Krasnoselskii and Krasnoselskii-Schaefer type fixed point theorems. Finally, some examples are given to illustrate the significance of our theoretical findings.Published under an exclusive license by AIP Publishing
Citation - WoS: 79
Citation - Scopus: 89
Existence Theory and Numerical Solutions To Smoking Model Under Caputo-Fabrizio Fractional Derivative
(Amer inst Physics, 2019) Shah, Kamal; Zaman, Gul; Jarad, Fahd; Khan, Sajjad Ali
In this paper, taking fractional derivative due to Caputo and Fabrizo, we have investigated a biological model of smoking type. By using Sumudu transform and Picard successive iterative technique, we develop the iterative solutions for the considered model. Furthermore, some results related to uniqueness of the equilibrium solution and its stability are discussed utilizing the techniques of nonlinear functional analysis. The dynamics of iterative solutions for various compartments of the model are plotted with the help of Matlab. Published under license by AIP Publishing.
Citation - WoS: 179
Citation - Scopus: 192
Fractional Modeling of Blood Ethanol Concentration System With Real Data Application
(Amer inst Physics, 2019) Yusuf, Abdullahi; Shaikh, Asif Ali; Inc, Mustafa; Baleanu, Dumitru; Qureshi, Sania
In this study, a physical system called the blood ethanol concentration model has been investigated in its fractional (non-integer) order version. The three most commonly used fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu fractional derivative in the Caputo sense-ABC and the Caputo-Fabrizio-CF) kernels have been used to fractionalize the model, whereas during the process of fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of squared residuals is carried out to show the performance of the models along with some graphical illustrations. Published under license by AIP Publishing.
Citation - WoS: 45
Citation - Scopus: 42
Mathematical Modeling for Adsorption Process of Dye Removal Nonlinear Equation Using Power Law and Exponentially Decaying Kernels
(Amer inst Physics, 2020) Yusuf, Abdullahi; Shaikh, Asif Ali; Inc, Mustafa; Baleanu, Dumitru; Qureshi, Sania
In this research work, a new time-invariant nonlinear mathematical model in fractional (non-integer) order settings has been proposed under three most frequently employed strategies of the classical Caputo, the Caputo-Fabrizio, and the Atangana-Baleanu-Caputo with the fractional parameter chi , where 0 < chi <= 1. The model consists of a nonlinear autonomous transport equation used to study the adsorption process in order to get rid of the synthetic dyeing substances from the wastewater effluents. Such substances are used at large scale by various industries to color their products with the textile and chemical industries being at the top. The non-integer-order model suggested in the present study depicts the past behavior of the concentration of the solution on the basis of having information of the initial concentration present in the dye. Being nonlinear, it carries the possibility to have no exact solution. However, the Lipchitz condition shows the existence and uniqueness of the underlying model's solution in non-integer-order settings. From a numerical simulation viewpoint, three numerical techniques having first order convergence have been employed to illustrate the numerical results obtained. Published under license by AIP Publishing.
Citation - WoS: 172
Citation - Scopus: 183
A New and Efficient Numerical Method for the Fractional Modeling and Optimal Control of Diabetes and Tuberculosis Co-Existence
(Amer inst Physics, 2019) Ghanbari, Behzad; Baleanu, Dumitru; Jajarmi, Amin
The main objective of this research is to investigate a new fractional mathematical model involving a nonsingular derivative operator to discuss the clinical implications of diabetes and tuberculosis coexistence. The new model involves two distinct populations, diabetics and nondiabetics, while each of them consists of seven tuberculosis states: susceptible, fast and slow latent, actively tuberculosis infection, recovered, fast latent after reinfection, and drug-resistant. The fractional operator is also considered a recently introduced one with Mittag-Leffler nonsingular kernel. The basic properties of the new model including non-negative and bounded solution, invariant region, and equilibrium points are discussed thoroughly. To solve and simulate the proposed model, a new and efficient numerical method is established based on the product-integration rule. Numerical simulations are presented, and some discussions are given from the mathematical and biological viewpoints. Next, an optimal control problem is defined for the new model by introducing four control variables reducing the number of infected individuals. For the control problem, the necessary and sufficient conditions are derived and numerical simulations are given to verify the theoretical analysis.
Citation - WoS: 132
Citation - Scopus: 130
New Fractional Derivatives With Non-Singular Kernel Applied To the Burgers Equation
(Amer inst Physics, 2018) Atangana, Abdon; Baleanu, Dumitru; Saad, Khaled M.
In this paper, we extend the model of the Burgers (B) to the new model of time fractional Burgers (TFB) based on Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Mittag-Leffler (ML) fractional time derivatives, respectively. We utilize the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of TFB using LC, CF, and ML in the Liouville-Caputo sense. We study the convergence analysis of HATM by computing the interval of the convergence, the residual error function (REF), and the average residual error (ARE), respectively. The results are very effective and accurate. Published by AIP Publishing.
Citation - WoS: 301
Citation - Scopus: 329
A New Fractional Model and Optimal Control of a Tumor-Immune Surveillance With Non-Singular Derivative Operator
(Amer inst Physics, 2019) Jajarmi, A.; Sajjadi, S. S.; Mozyrska, D.; Baleanu, D.
In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined. Published under license by AIP Publishing.
Citation - WoS: 237
Citation - Scopus: 247
New Variable-Order Fractional Chaotic Systems for Fast Image Encryption
(Amer inst Physics, 2019) Deng, Zhen-Guo; Baleanu, Dumitru; Zeng, De-Qiang; Wu, Guo-Cheng
New variable-order fractional chaotic systems are proposed in this paper. A concept of short memory is introduced where the initial point in the Caputo derivative is varied. The fractional order is defined by the use of a piecewise constant function which leads to rich chaotic dynamics. The predictor-corrector method is adopted, and numerical solutions of fractional delay equations are obtained. Then, this concept is extended to fractional difference equations, and generalized chaotic behaviors are discussed numerically. Finally, the new fractional chaotic models are applied to block image encryption and each block has a different fractional order. The new chaotic system improves security of the image encryption and saves the encryption time greatly. Published under license by AIP Publishing.
Citation - WoS: 114
Citation - Scopus: 108
Numerical Solutions of the Fractional Fisher's Type Equations With Atangana-Baleanu Fractional Derivative by Using Spectral Collocation Methods
(Amer inst Physics, 2019) Khader, M. M.; Gomez-Aguilar, J. F.; Baleanu, Dumitru; Saad, K. M.
The main objective of this paper is to investigate an accurate numerical method for solving a biological fractional model via Atangana-Baleanu fractional derivative. We focused our attention on linear and nonlinear Fisher's equations. We use the spectral collocation method based on the Chebyshev approximations. This method reduced the nonlinear equations to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them by using the finite difference method. This is the first time that this method is used to solve nonlinear equations in Atangana-Baleanu sense. We present the effectiveness and accuracy of the proposed method by computing the absolute error and the residual error functions. The results show that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.
Citation - WoS: 203
Citation - Scopus: 210
On Exact Traveling-Wave Solutions for Local Fractional Korteweg-De Vries Equation
(Aip Publishing, 2016) Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo; Yang, Xiao-Jun
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces. Published by AIP Publishing.
Citation - WoS: 107
Citation - Scopus: 118
On the Analysis of Chemical Kinetics System Pertaining To a Fractional Derivative With Mittag-Leffler Type Kernel
(Aip Publishing, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
The pivotal aim of this paper was to analyze a new fractional model of chemical kinetics system related to a newly discovered Atangana-Baleanu derivative with fractional order having non-singular and non-local kernel. The numerical solution is derived by making use of the iterative scheme. The existence of the solution of chemical kinetics system of arbitrary order is examined by implementing the fixed-point theorem. The uniqueness of the special solution of the studied model is shown. The effect of different variables and order of arbitrary ordered derivative on concentrations is demonstrated in tabular and graphical forms. The numerical results for chemical kinetics system pertaining to the newly derivative with fractional order are compared with the chemical kinetics system involving classical derivative. Published by AIP Publishing.
Citation - WoS: 4
Citation - Scopus: 4
Preface: Recent Advances in Fractional Dynamics
(Amer inst Physics, 2016) Baleanu, Dumitru; Li, Changpin; Srivastava, H. M.
This Special Focus Issue contains several recent developments and advances on the subject of Fractional Dynamics and its widespread applications in various areas of the mathematical, physical, and engineering sciences. Published by AIP Publishing.
Citation - WoS: 14
Citation - Scopus: 12
Representation of Solutions for Sturm-Liouville Eigenvalue Problems With Generalized Fractional Derivative
(Amer inst Physics, 2020) Bas, Erdal; Baleanu, Dumitru; Ozarslan, Ramazan
We analyze fractional Sturm-Liouville problems with a new generalized fractional derivative in five different forms. We investigate the representation of solutions by means of rho-Laplace transform for generalized fractional Sturm-Liouville initial value problems. Finally, we examine eigenfunctions and eigenvalues for generalized fractional Sturm-Liouville boundary value problems. All results obtained are compared with simulations in detail under different alpha fractional orders and real rho values. Published under license by AIP Publishing.
Citation - WoS: 37
Citation - Scopus: 37
Riesz Riemann-Liouville Difference on Discrete Domains
(Aip Publishing, 2016) Baleanu, Dumitru; Xie, He-Ping; Wu, Guo-Cheng
A Riesz difference is defined by the use of the Riemann-Liouville differences on time scales. Then the definition is considered for discrete fractional modelling. A lattice fractional equation method is proposed among which the space variable is defined on discrete domains. Finite memory effects are introduced into the lattice system and the numerical formulae are given. Adomian decomposition method is adopted to solve the fractional partial difference equations numerically. Published by AIP Publishing.
Citation - WoS: 30
Citation - Scopus: 32
Spatio-Temporal Numerical Modeling of Reaction-Diffusion Measles Epidemic System
(Aip Publishing, 2019) Wei, Zhouchao; Baleanu, Dumitru; Rafiq, M.; Rehman, M. A.; Ahmed, Nauman
In this work, we investigate the numerical solution of the susceptible exposed infected and recovered measles epidemic model. We also evaluate the numerical stability and the bifurcation value of the transmission parameter from susceptibility to a disease of the proposed epidemic model. The proposed method is a chaos free finite difference scheme, which also preserves the positivity of the solution of the given epidemic model. Published under license by AIP Publishing.
Citation - WoS: 20
Citation - Scopus: 21
Stability Analysis and Numerical Simulations of Spatiotemporal Hiv Cd4+t Cell Model With Drug Therapy
(Amer inst Physics, 2020) Elsonbaty, Amr; Adel, Waleed; Baleanu, Dumitru; Rafiq, Muhammad; Ahmed, Nauman
In this study, an extended spatiotemporal model of a human immunodeficiency virus (HIV) CD4+ T cell with a drug therapy effect is proposed for the numerical investigation. The stability analysis of equilibrium points is carried out for temporal and spatiotemporal cases where stability regions in the space of parameters for each case are acquired. Three numerical techniques are used for the numerical simulations of the proposed HIV reaction-diffusion system. These techniques are the backward Euler, Crank-Nicolson, and a proposed structure preserving an implicit technique. The proposed numerical method sustains all the important characteristics of the proposed HIV model such as positivity of the solution and stability of equilibria, whereas the other two methods have failed to do so. We also prove that the proposed technique is positive, consistent, and Von Neumann stable. The effect of different values for the parameters is investigated through numerical simulations by using the proposed method. The stability of the proposed model of the HIV CD4+ T cell with the drug therapy effect is also analyzed.
Citation - WoS: 123
Citation - Scopus: 124
Two-Strain Epidemic Model Involving Fractional Derivative With Mittag-Leffler Kernel
(Aip Publishing, 2018) Qureshi, Sania; Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Shaikh, Asif Ali; Yusuf, Abdullahi
In the present study, the fractional version with respect to the Atangana-Baleanu fractional derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu fractional derivative operator in the caputo sense. To believe upon the results obtained, the fractional order alpha has been allowed to vary between (0, 1], whereupon the physical observations match with those obtained in the classical case, but the fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of fractional order derivatives for ABC. Finally, the fractional forward Euler method in the classical caputo sense has been used to illustrate the better performance of the numerical method obtained via the Atangana-Baleanu fractional derivative operator in the caputo sense. Published by AIP Publishing.

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