What is it about?

In this paper, we apply Legendre-Laguerre functions (LLFs) and the 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.

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Why is it important?

This work introduces a new numerical approach for solving VO-TF-PIDEs with the weakly singular kernel. The method is based on expanding the derivation of the solution in terms of the LLFs and using the appropriate collocation points. The main objective is to use an integral pseudo-operational matrix of LLFs, which provides good conditions to receive the approximate solution with high accuracy. The advantage of the proposed method is that, despite defined time in an infinite interval, we achieved a good approximate solution.

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This page is a summary of: NUMERICAL SOLUTION OF VARIABLE-ORDER TIME FRACTIONAL WEAKLY SINGULAR PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH ERROR ESTIMATION, Mathematical Modelling and Analysis, October 2020, Vilnius Gediminas Technical University,
DOI: 10.3846/mma.2020.11692.
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