The moving least square method for solving the time fractional partial integro-differential equation of Volterra type and its convergence analysis

Volume 37, Issue 2, pp 236--260 https://dx.doi.org/10.22436/jmcs.037.02.08

Publication Date: September 25, 2024 Submission Date: February 03, 2024 Revision Date: May 15, 2024 Accteptance Date: August 24, 2024

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Authors

S. Elbostani - MISI Laboratory‎, ‎Faculty of Sciences and Technology, ‎Hassan \(1^{\rm er}\) University, ‎Settat, ‎Morocco. A. Mohib - Laboratoire LMAI‎, ‎ENS de Casablanca, ‎Hassan II university of Casablanca, ‎B.P‎. ‎50069‎, ‎Ghandi Casablanca, ‎Morocco. R. El Jid - MISI Laboratory‎, ‎Faculty of Sciences and Technology, ‎Hassan \(1^{\rm er}\) University, ‎Settat, ‎Morocco. A. Rachid - Laboratoire LMAI‎, ‎ENS de Casablanca, Hassan II university of Casablanca, B.P‎. ‎50069‎, ‎Ghandi Casablanca, ‎Morocco. Z. El Majouti - MISI Laboratory‎, ‎Faculty of Sciences and Technology, Hassan \(1^{\rm er}\) University, ‎Settat, ‎Morocco.

Abstract

In this paper‎, ‎the moving least square (MLS) approximation is implemented for the numerical solution of time fractional partial integro-differential equation (TFPIDE) on a bounded domain‎. ‎To establish the scheme‎, ‎we apply the finite difference scheme to approximate the time Caputo fractional derivative‎, ‎and we employ the composite trapezoidal quadrature rule for estimating integrals‎. ‎This approach is very convenient for solving TFPIDE since it does not require any need for mesh connectivity‎. ‎Then‎, ‎the problem solving turns into solution of a linear system‎. ‎The applicability and the validity of this method is investigated‎. ‎Furthermore‎, ‎the error estimate of the proposed method is provided‎. ‎Finally‎, ‎several numerical problems are solved which confirmed the theoretical findings‎. ‎

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Keywords

• Fractional partial integro-differential equation (FPIDE)
• moving least squares (MLS)
• Caputo fractional derivative
• convergence analysis

MSC

•  26A33
•  35R09
•  45D05
•  45K05
•  ‎65A05
•  65N35

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