Browsing by Author "Ilie, Mousa"

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Citation Count: Hosseini, Kamyar...et al. (2021). "An analytic study on the approximate solution of a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law", Mathematical Methods in the Applied Sciences, Vol. 44, no. 8, pp. 6247-6258.
An analytic study on the approximate solution of a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law
(2021) Hosseini, Kamyar; Ilie, Mousa; Mirzazadeh, Mohammad; Baleanu, Dumitru; 56389
The main aim of the current article is considering a nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law and deriving its approximate analytical solution in a systematic way. More precisely, after reformulating the nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law, its approximate analytical solution is derived formally through the use of the homotopy analysis transform method (HATM) which is based on the homotopy method and the Laplace transform. The existence and uniqueness of the solution of the nonlinear time-fractional Cauchy reaction-diffusion equation with the Mittag-Leffler law are also studied by adopting the fixed-point theorem. In the end, by considering some two- and three-dimensional graphs, the influence of the order of time-fractional operator on the displacement is examined in detail.
Citation Count: Hosseini, Kamyar...et al. (20219. "An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense", Mathematics and Computers in Simulation, Vol. 187, pp. 248-260.
An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense
(2021) Hosseini, Kamyar; Ilie, Mousa; Mirzazadeh, Mohammad; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadi; Baleanu, Dumitru; Salahshour, Soheil; 56389
The authors' concern of the present paper is to conduct a systematic study on a time-fractional nonlinear water wave equation which is an evolutionary version of the Boussinesq system. The study goes on by adopting a new analytical method based on the Laplace transform and the homotopy analysis method to the governing model and obtaining its approximate solutions in the presence of the Caputo fractional derivative. To analyze the influence of the Caputo operator on the dynamical behavior of the approximate solutions, some graphical illustrations in two- and three-dimensions are formally presented. Furthermore, several numerical tables are given to support the performance of the new analytical method in handling the time-fractional nonlinear water wave equation. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Citation Count: Hosseini, Kamyar...et.al. (2022). "The Caputo-Fabrizio time-fractional Sharma-Tasso-Olver-Burgers equation and its valid approximations", Communications in Theoretical Physics, Vol.74, No.7.
The Caputo-Fabrizio time-fractional Sharma-Tasso-Olver-Burgers equation and its valid approximations
(2022) Hosseini, Kamyar; Ilie, Mousa; Mirzazadeh, Mohammad; Baleanu, Dumitru; Park, Choonkil; Salahshour, Soheil; 56389
Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention, in the last decades. The main aim of the current investigation is to consider the time-fractional Sharma-Tasso-Olver-Burgers (STOB) equation in the Caputo-Fabrizio (CF) context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method (HAM) and the Laplace transform. The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition for φx,t;u as the kernel and giving some theorems. To illustrate the CF operator effect on the dynamics of the obtained solitons, several two- and three-dimensional plots are formally considered. It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context.