A tau method based on Jacobi operational matrix for solving fractional telegraph equation with Riesz-space derivative

2020 ◽  
Vol 39 (4) ◽  
Author(s):  
Samira Bonyadi ◽  
Yaghoub Mahmoudi ◽  
Mehrdad Lakestani ◽  
Mohammad Jahangiri Rad
2022 ◽  
Vol 40 ◽  
pp. 1-13
Author(s):  
Fakhrodin Mohammadi ◽  
Hossein Hassani

‎In this article‎, ‎an efficient numerical method based on a new class of orthogonal polynomials‎, ‎namely Chelyshkov polynomials‎, ‎has been presented to approximate solution of time-fractional telegraph (TFT) equations‎. ‎The fractional operational matrix of the Chelyshkov polynomials along with the typical collocation method is used to reduces TFT equations to a system of algebraic equations‎. ‎The error analysis of the proposed collocation method is also investigated‎. ‎A comparison with other published results confirms that the presented Chelyshkov collocation approach is efficient and accurate for solving TFT equations‎. ‎Illustrative examples are included to demonstrate the efficiency of the Chelyshkov method‎.


2019 ◽  
Vol 4 (6) ◽  
pp. 1664-1683
Author(s):  
S. Mohammadian ◽  
◽  
Y. Mahmoudi ◽  
F. D. Saei

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1264
Author(s):  
Vladimir V. Uchaikin ◽  
Renat T. Sibatov ◽  
Dmitry N. Bezbatko

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.


Author(s):  
Orkun Tasbozan ◽  
Alaattin Esen

Abstract In this study, we investigate numerical solutions of the fractional telegraph equation with the aid of cubic B-spline collocation method. The fractional derivatives have been considered in the Caputo forms. The L1and L2 formulae are used to discretize the Caputo fractional derivative with respect to time. Some examples have been given for determining the accuracy of the regarded method. Obtained numerical results are compared with exact solutions arising in the literature and the error norms L 2 and L ∞ have been computed. In addition, graphical representations of numerical results are given. The obtained results show that the considered method is effective and applicable for obtaining the numerical results of nonlinear fractional partial differential equations (FPDEs).


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