This article is cited in 7 papers

Numerical solution for a variable-order fractional nonlinear cable equation via Chebyshev cardinal functions

Somayeh Abdi-Mazraeh^a, Safar Irandoust-Pakchin^b, Ali Khani<sup>a

a</sup> Department of Sciences, Azarbaijan Shahid Madani University, Tabriz, Iran
^b Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

Abstract: In this paper, a variable-order fractional derivative nonlinear cable equation is considered. It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of class of fractional partial differential equation with variable coefficient of fractional differential equation in various continues functions of spatial and time orders. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. Finally, illustrative examples are included to demonstrate the validity and applicability of the presented technique.

Key words: operational matrix of fractional derivative, variable-order fractional derivative, Caputo derivative, nonlinear cable equation, Riemann–Liouville derivative.

UDC: 519.62

Received: 21.01.2015

Language: English

DOI: 10.7868/S0044466917120134

 English version: Computational Mathematics and Mathematical Physics, 2017, 57:12, 2047–2056

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