WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 20Citation - Scopus: 23A Pseudo-Operational Collocation Method for Variable-Order Time-Space Fractional Kdv-Burgers Equation(Wiley, 2023) Hosseini, Kamyar; Hincal, Evren; Baleanu, Dumitru; Salahshour, Soheil; Sadri, KhadijehThe idea of this work is to provide a pseudo-operational collocation scheme to deal with the solution of the variable-order time-space fractional KdV-Burgers-Kuramoto equation (VOSTFKBKE). Such the fractional partial differential equation (FPDE) has three characteristics of dissipation, dispersion, and instability, which make this equation is used to model many phenomena in diverse fields of physics. Numerical solutions are sought in a linear combination of two-dimensional Jacobi polynomials as basis functions. In order to approximate unknown functions in terms of the basis vector, pseudo-operational matrices are constructed to avoid integration. An error bound of the residual function is estimated in a Jacobi-weighted space in the L2$$ {L}<^>2 $$ norms. Numerical results are compared with exact ones and those reported by other researchers to demonstrate the effectiveness of the recommended method.Article Citation - WoS: 38Citation - Scopus: 43An Analytic Study on the Approximate Solution of a Nonlinear Time-Fractional Cauchy Reaction-Diffusion Equation With the Mittag-Leffler Law(Wiley, 2021) Ilie, Mousa; Mirzazadeh, Mohammad; Baleanu, Dumitru; Hosseini, KamyarThe 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.