Numerical solution of variable-order time fractional weakly singular partial integro-differential equations with error estimation - Dehestani, Haniye; Ordokhani, Yadollah; Razzaghi, Mohsen (Mathematical Modelling and Analysis, 2020)
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.