Fall 2023 A NOVEL METHOD FOR LINEAR AND NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS VIA CUBIC HAT FUNCTIONS
Hamed Ebrahimi, Jafar Biazar
J. Integral Equations Applications 35(3): 291-310 (Fall 2023). DOI: 10.1216/jie.2023.35.291

Abstract

In this study, a new numerical algorithm is proposed for solving a class of nonlinear fractional Volterra integral equations of the second kind based on our newly constructed hat functions. New functions that are called cubic hat functions (CHFs) and operational matrices of fractional order integration of these functions are applied. In a new numerical approach, the fractional order operational matrix of CHFs and the powers of weakly singular kernels of integral equations are handed down as a structure for converting the principal problem into a number of systems containing three-variable polynomial equations. Also, error analysis, convergence analysis of this method and convergence rate are investigated. In the last part, the high precision of the utilized method is shown with three examples. In addition, comparisons with Jacobi spectral Galerkin and modified hat functions methods demonstrate the improved performance of the presented approach.

Citation

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Hamed Ebrahimi. Jafar Biazar. "A NOVEL METHOD FOR LINEAR AND NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS VIA CUBIC HAT FUNCTIONS." J. Integral Equations Applications 35 (3) 291 - 310, Fall 2023. https://doi.org/10.1216/jie.2023.35.291

Information

Received: 26 December 2022; Revised: 29 March 2023; Accepted: 30 May 2023; Published: Fall 2023
First available in Project Euclid: 25 October 2023

Digital Object Identifier: 10.1216/jie.2023.35.291

Subjects:
Primary: 26A33 , 33Exx , 44Axx , 65D15

Keywords: cubic hat functions , fractional Volterra integral equations , new fractional order operational matrix , new methodology

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.35 • No. 3 • Fall 2023
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