Mathematics and Computational Sciences

A modification on Ritz method and least squares approach for a class of fractional integro-differential equations

Articles in Press

Document Type : Original Article

Authors

Khosro Sayevand 1
Mohammadreza Rostami 2

1 Department of Mathematics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, IRAN

2 Faculty of Mathematical Sciences‎, ‎Malayer University‎, ‎P‎. ‎O‎. ‎Box 16846-13114‎, ‎Malayer‎, ‎Iran‎

https://doi.org/10.30511/mcs.2026.2080055.1654
Abstract
The modeling of many problems in science and engineering often leads to integro-differential equations‎.
‎In recent years‎, ‎these equations have been increasingly formulated using various types of fractional derivatives‎.
‎In most cases‎, ‎there exists no specific analytical method to obtain accurate solutions for such equations‎.
‎Therefore‎, ‎the study of numerical and approximate techniques for solving fractional integro-differential equations (FIDEs) has become an active research area‎.
‎In the present work‎, ‎a new strategy is proposed for solving FIDEs involving Caputo-type fractional derivatives‎.
‎The approach employs fractional-order shifted Legendre functions as the approximation basis‎, ‎combined with a modified Ritz method and the least-squares technique to ensure stability and accuracy‎.
‎Error analysis and convergence properties are established‎, ‎and several numerical examples are presented to demonstrate the effectiveness and superiority of the proposed method compared with existing techniques.

Keywords

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Fractional-order&lrm
Least square approximation method&lrm
Ritz method&lrm
, &lrm
Fractional integro-differential equation
Subjects
Mathematics and Computational Sciences

Articles in Press, Accepted Manuscript
Available Online from 16 October 2026

  • Receive Date 06 December 2025
  • Revise Date 05 May 2026
  • Accept Date 11 May 2026

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