Numerical Solution of Space-time Fractional two-dimensional Telegraph Equation by Shifted Legendre Operational Matrices
author
Abstract:
Fractional differential equations (FDEs) have attracted in the recent years a considerable interest due to their frequent appearance in various fields and their more accurate models of systems under consideration provided by fractional derivatives. For example, fractional derivatives have been used successfully to model frequency dependent damping behavior of many viscoelastic materials. They are also used in modeling of many chemical processed, mathematical biology and many other problems in engineering. The history and a comprehensive treatment of FDEs are provided by Podlubny and a review of some applications of FDEs are given by Mainardi. ./files/site1/files/41/4Extended_Abstract(1).pdf
similar resources
Analytical solution for a generalized space-time fractional telegraph equation
In this paper, we consider a nonhomogeneous space-time fractional telegraph equation defined in a bounded space domain, which is obtained from the standard telegraph equation by replacing the firstor second-order time derivative by the Caputo fractional derivative Dt , α > 0; and the Laplacian operator by the fractional Laplacian (−∆) , β ∈ (0, 2]. We discuss and derive the analytical solutions...
full textApplication of Legendre operational matrix to solution of two dimensional nonlinear Volterra integro-differential equation
In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...
full textLegendre wavelets method for numerical solution of time-fractional heat equation
In this paper, we develop an efficient Legend...
full textNumerical Solution of Fractional Telegraph Equation via the Tau Method
This paper presents a computational technique based on the Tau method and Legendre polynomials for the solution of a class of time-fractional telegraph equations. An appropriate representation of the solution via the Legendre operational matrix of fractional derivative is used to reduces its numerical treatment to the solution of a set of linear algebraic equations. The fractional derivatives a...
full textSolution of Space-time Fractional Telegraph Equation by Adomian Decomposition Method
In the present paper we obtain closed form solutions of spacetime fractional telegraph equations using Adomian decomposition method. The space and time fractional derivatives are considered as Caputo fractional derivative and the solutions are obtained in terms of Mittag-Leffler functions.
full textA numerical scheme for space-time fractional advection-dispersion equation
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...
full textMy Resources
Journal title
volume 4 issue 1
pages 45- 62
publication date 2018-08
By following a journal you will be notified via email when a new issue of this journal is published.
No Keywords
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023