Next Article in Journal
Optimized Procedure to Schedule Physicians in an Intensive Care Unit: A Case Study
Next Article in Special Issue
State Feedback Regulation Problem to the Reaction-Diffusion Equation
Previous Article in Journal
The Optimal Control of Government Stabilization Funds
Previous Article in Special Issue
Boundary Control for a Certain Class of Reaction-Advection-Diffusion System
Article

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

1
Department of Mathematics, Islamia College Peshawar, Peshawar 25000, Khyber Pakhtoon Khwa, Pakistan
2
Department of Mathematics, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan
3
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
4
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
5
College of Science Department of Mathematics, Northern Border University, Arar 73222, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 1972; https://doi.org/10.3390/math8111972
Received: 8 October 2020 / Revised: 1 November 2020 / Accepted: 3 November 2020 / Published: 6 November 2020
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering)
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. View Full-Text
Keywords: fractional partial integro differential; weakly singular kernel; Laplace transform; local meshless method; contour integration; Talbot’s contour; midpoint rule fractional partial integro differential; weakly singular kernel; Laplace transform; local meshless method; contour integration; Talbot’s contour; midpoint rule
Show Figures

Figure 1

MDPI and ACS Style

Kamran, K.; Shah, Z.; Kumam, P.; Alreshidi, N.A. A Meshless Method Based on the Laplace Transform for the 2D Multi-Term Time Fractional Partial Integro-Differential Equation. Mathematics 2020, 8, 1972. https://doi.org/10.3390/math8111972

AMA Style

Kamran K, Shah Z, Kumam P, Alreshidi NA. A Meshless Method Based on the Laplace Transform for the 2D Multi-Term Time Fractional Partial Integro-Differential Equation. Mathematics. 2020; 8(11):1972. https://doi.org/10.3390/math8111972

Chicago/Turabian Style

Kamran, Kamran, Zahir Shah, Poom Kumam, and Nasser A. Alreshidi. 2020. "A Meshless Method Based on the Laplace Transform for the 2D Multi-Term Time Fractional Partial Integro-Differential Equation" Mathematics 8, no. 11: 1972. https://doi.org/10.3390/math8111972

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop