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...
Saved in:
| Published in: | Majallat Jāmiʻat Bābil pp. 83 - 106 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
14.10.2025
|
| ISSN: | 1992-0652, 2312-8135 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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 |