A Midpoint Quadratic Approach for Solving Numerically Multi-Order Fractional Integro-Differential Equation

Background: This article presents a method for finding numerical solutions to Fredholm integro-differential equations (FIFDEs) with multi-fractional orders of one or less, using a useful algorithm. Materials and Methods:  A finite difference approximation to Caputo's derivative using collocatio...

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Bibliographic Details
Published in:Majallat Jāmiʻat Bābil pp. 83 - 106
Main Authors: Zahir, Dashne Chapuk, Ahmed, Shazad Shawki, Mohammedfaeq, Shabaz Jalil
Format: Journal Article
Language:English
Published: 14.10.2025
ISSN:1992-0652, 2312-8135
Online Access:Get full text
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Summary:Background: This article presents a method for finding numerical solutions to Fredholm integro-differential equations (FIFDEs) with multi-fractional orders of one or less, using a useful algorithm. Materials and Methods:  A finite difference approximation to Caputo's derivative using collocation points is used to build the midpoint method for the quadrature rule, which forms the basis of the approach. Results: Our method simplifies the evaluation of treatments by transforming the FIFDEs into algebraic equations with operational matrices. After calculating the Caputo derivative at a specific point using the finite difference method, we use the quadrature method, which includes the midpoint rule, to create a finite difference formula for our fractional equation. Conclusions: Additionally, numerical examples are provided to demonstrate the validity and use of the approach as well as comparisons with earlier findings. The results are expressed using a program created in MATLAB.  
ISSN:1992-0652
2312-8135
DOI:10.29196/jubpas.v33i3.5974