A finite difference technique for solving variable-order‎ ‎fractional integro-differential equations

Xu, Yufeng; Suat Ertürk, Vedat

A finite difference technique for solving variable-order‎ ‎fractional integro-differential equations

Document Type : Research Paper

Authors

Yufeng Xu ¹
Vedat Suat Ertürk ²

¹ Department of Applied Mathematics, Central South University, Changsha, People’s Republic of China

² Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayıs University, 55139, Samsun, Turkey

Abstract

‎In this article‎, we use a finite difference technique‎ ‎to solve variable-order fractional integro-differential equations‎ ‎(VOFIDEs‎, ‎for short)‎. ‎In these equations‎, ‎the variable-order fractional integration(VOFI) and‎ ‎variable-order fractional derivative (VOFD) are described in the‎ ‎Riemann-Liouville's and Caputo's sense,respectively‎. ‎Numerical experiments‎, ‎consisting of two examples‎, ‎are‎ ‎studied‎. ‎The obtained numerical results reveal that the proposed finite difference technique is‎ ‎very effective and convenient for solving VOFIDEs‎.

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