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Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation

    Haniye Dehestani   Affiliation
    ; Yadollah Ordokhani   Affiliation
    ; Mohsen Razzaghi   Affiliation

Abstract

In this paper, we apply Legendre-Laguerre functions (LLFs) and collocation method to obtain the approximate solution of variable-order time-fractional partial integro-differential equations (VO-TF-PIDEs) with the weakly singular kernel. For this purpose, we derive the pseudo-operational matrices with the use of the transformation matrix. The collocation method and pseudo-operational matrices transfer the problem to a system of algebraic equations. Also, the error analysis of the proposed method is given. We consider several examples to illustrate the proposed method is accurate.

Keyword : variable-order fractional partial integro-differential equations, weakly singular kernel, Legendre-Laguerre functions, pseudo-operational matrix

How to Cite
Dehestani, H., Ordokhani, Y., & Razzaghi, M. (2020). Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation. Mathematical Modelling and Analysis, 25(4), 680-701. https://doi.org/10.3846/mma.2020.11692
Published in Issue
Oct 13, 2020
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