A new wavelet method for fractional integro-differential equations with ψ-Caputo fractional derivative

M.H. Heydari and M. Razzaghi

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 217, issue C, 97-108

Abstract: In this work, the ψ-Caputo fractional derivative is successfully used to define a new class of nonlinear fractional integro-differential equations. The extended Chebyshev cardinal wavelets (CCWs), as a proper set of wavelet functions, are employed to establish a computational procedure for such equations. To do this, a new operational matrix for the ψ-Riemann–Liouville fractional integral of the extended CCWs is extracted with the help of the block-pulse functions. The established approach obtains the problem solution by solving an algebraic system of nonlinear equations that is created from expanding the solution by the extended CCWs (with some unknown coefficients) and utilizing the expressed fractional operational matrix. In fact, by solving this system, the unknown coefficients and, subsequently the solution of the original problem are obtained. The convergence analysis of the proposed method is investigated. The accuracy and correctness of the scheme are illustrated by solving three examples.

Keywords: ψ-Riemann–Liouville fractional integral; ψ-Caputo fractional derivative; Fractional integro-differential equations; Extended Chebyshev cardinal wavelets; Block-pulse functions. (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:217:y:2024:i:c:p:97-108

DOI: 10.1016/j.matcom.2023.10.023

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