A Meshless Method Based on the Laplace Transform for the 2D Multi-Term Time Fractional Partial Integro-Differential Equation

Kamran Kamran, Zahir Shah, Poom Kumam and Nasser Aedh Alreshidi
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Kamran Kamran: Department of Mathematics, Islamia College Peshawar, Peshawar 25000, Khyber Pakhtoon Khwa, Pakistan
Zahir Shah: Department of Mathematics, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan
Poom Kumam: KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
Nasser Aedh Alreshidi: College of Science Department of Mathematics, Northern Border University, Arar 73222, Saudi Arabia

Mathematics, 2020, vol. 8, issue 11, 1-14

Abstract: In this article, we propose a localized transform based meshless method for approximating the solution of the 2D multi-term partial integro-differential equation involving the time fractional derivative in Caputo’s sense with a weakly singular kernel. The purpose of coupling the localized meshless method with the Laplace transform is to avoid the time stepping procedure by eliminating the time variable. Then, we utilize the local meshless method for spatial discretization. The solution of the original problem is obtained as a contour integral in the complex plane. In the literature, numerous contours are available; in our work, we will use the recently introduced improved Talbot contour. We approximate the contour integral using the midpoint rule. The bounds of stability for the differentiation matrix of the scheme are derived, and the convergence is discussed. The accuracy, efficiency, and stability of the scheme are validated by numerical experiments.

Keywords: fractional partial integro differential; weakly singular kernel; Laplace transform; local meshless method; contour integration; Talbot’s contour; midpoint rule (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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