WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 15Citation - Scopus: 14Designing a Matrix Collocation Method for Fractional Delay Integro-Differential Equations With Weakly Singular Kernels Based on Vieta-Fibonacci Polynomials(Mdpi, 2022) Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Park, Choonkil; Sadri, KhadijehIn the present work, the numerical solution of fractional delay integro-differential equations (FDIDEs) with weakly singular kernels is addressed by designing a Vieta-Fibonacci collocation method. These equations play immense roles in scientific fields, such as astrophysics, economy, control, biology, and electro-dynamics. The emerged fractional derivative is in the Caputo sense. By resultant operational matrices related to the Vieta-Fibonacci polynomials (VFPs) for the first time accompanied by the collocation method, the problem taken into consideration is converted into a system of algebraic equations, the solving of which leads to an approximate solution to the main problem. The existence and uniqueness of the solution of this category of fractional delay singular integro-differential equations (FDSIDEs) are investigated and proved using Krasnoselskii's fixed-point theorem. A new formula for extracting the VFPs and their derivatives is given, and the orthogonality of the derivatives of VFPs is easily proved via it. An error bound of the residual function is estimated in a Vieta-Fibonacci-weighted Sobolev space, which shows that by properly choosing the number of terms of the series solution, the approximation error tends to zero. Ultimately, the designed algorithm is examined on four FDIDEs, whose results display the simple implementation and accuracy of the proposed scheme, compared to ones obtained from previous methods. Furthermore, the orthogonality of the VFPs leads to having sparse operational matrices, which makes the execution of the presented method easy.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: 20Citation - Scopus: 24The (2+1)-Dimensional Hyperbolic Nonlinear Schrodinger Equation and Its Optical Solitons(Amer inst Mathematical Sciences-aims, 2021) Hosseini, Kamyar; Salahshour, Soheil; Sadri, Khadijeh; Mirzazadeh, Mohammad; Park, Choonkil; Ahmadian, Ali; Baleanu, Umitru; Baleanu, DumitruA comprehensive study on the (2+1)-dimensional hyperbolic nonlinear Schrodinger (2D-HNLS) equation describing the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics is conducted in the current paper. To this end, after reducing the 2D-HNLS equation to a one-dimensional nonlinear ordinary differential (1D-NLOD) equation in the real regime using a traveling wave transformation, its optical solitons are formally obtained through a group of well-established methods such as the exponential and Kudryashov methods. Some graphical representations regarding optical solitons that are categorized as bright and dark solitons are considered to clarify the dynamics of the obtained solutions. It is noted that some of optical solitons retrieved in the current study are new and have been not retrieved previously.Article Citation - WoS: 11Citation - Scopus: 17Bivariate Chebyshev Polynomials of the Fifth Kind for Variable-Order Time-Fractional Partial Integro-Differential Equations With Weakly Singular Kernel(Springer, 2021) Hosseini, Kamyar; Baleanu, Dumitru; Ahmadian, Ali; Salahshour, Soheil; Sadri, KhadijehThe shifted Chebyshev polynomials of the fifth kind (SCPFK) and the collocation method are employed to achieve approximate solutions of a category of the functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for the numerical solution of the problem under study. The suggested method changes solving the VTFWSPIDE into the solution of a system of linear algebraic equations. Error bounds of the approximate solutions are obtained, and the application of the proposed scheme is examined on five problems. The results confirm the applicability and high accuracy of the method for the numerical solution of fractional singular partial integro-differential equations.Article Citation - WoS: 37Citation - Scopus: 45An Effective Computational Method To Deal With a Time-Fractional Nonlinear Water Wave Equation in the Caputo Sense(Elsevier, 2021) Ilie, Mousa; Mirzazadeh, Mohammad; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadir; Baleanu, Dumitru; Salahshour, Soheil; Hosseini, KamyarThe 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.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.