Spectral technique for solving variable‐order fractional Volterra integro‐differential equations

• Published in: Numerical methods for partial differential equations Vol. 34; no. 5; pp. 1659 - 1677
• Main Authors: Doha, E. H., Abdelkawy, M. A., Amin, A. Z. M., Baleanu, D.
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc 01.09.2018
• Subjects: Differential equations; fractional calculus; Integro‐differential equation; Mathematical analysis; Riemann‐Liouville fractional of variable order; shifted Legendre‐Gauss‐Lobatto quadrature; spectral collocation method; Volterra integral equations
• ISSN: 0749-159X; 1098-2426
• DOI: 10.1002/num.22233

This article, presented a shifted Legendre Gauss‐Lobatto collocation (SL‐GL‐C) method which is introduced for solving variable‐order fractional Volterra integro‐differential equation (VO‐FVIDEs) subject to initial or nonlocal conditions. Based on shifted Legendre Gauss‐Lobatto (SL‐GL) quadrature, we treat with integral term in the aforementioned problems. Via the current approach, we convert such problem into a system of algebraic equations. After that we obtain the spectral solution directly for the proposed problem. The high accuracy of the method was proved by several illustrative examples.