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

• Main Authors: Haniye Dehestani, Yadollah Ordokhani, Mohsen Razzaghi
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2020-10-01
• Series: Mathematical Modelling and Analysis
• Subjects: variable-order fractional partial integro-differential equations; weakly singular kernel; Legendre-Laguerre functions; pseudo-operational matrix
• Online Access: https://www.bjrbe.vgtu.lt/index.php/MMA/article/view/11692
• ISSN: 1392-6292; 1648-3510

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.