A Midpoint Quadratic Approach for Solving Numerically Multi-Order Fractional Integro-Differential Equation | مجلة جامعة بابل - للعلوم الصرفه والتطبيقية

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منشور: 2025-10-14

DOI: https://doi.org/10.29196/jubpas.v33i3.5974

الكلمات المفتاحية:

Fractional calculus، Caputo-fractional derivative، integral-differential equation, midpoint rules، forward difference approximation

Dashne Chapuk Zahir

Department of Mathematics, Faculty of Science and Health, Koya University, Koya 46017, Iraq

Shazad Shawki Ahmed

Department of Mathematics, College of Science, Sulaimani University, Sulaymaniyah 46001, Iraq

Shabaz Jalil Mohammedfaeq

Department of Mathematics, College of Science, Sulaimani University, Sulaymaniyah 46001, Iraq;

الملخص

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.

إصدار

Vol.33 ; No. 3 ( 2025)

القسم

Articles

Creative Commons License

هذا العمل مرخص بموجب Creative Commons Attribution 4.0 International License.

كيفية الاقتباس

[1]

"A Midpoint Quadratic Approach for Solving Numerically Multi-Order Fractional Integro-Differential Equation ", JUBPAS, م 33, عدد 3, ص 83–106, 2025, doi: 10.29196/jubpas.v33i3.5974.

المؤلفات المشابهة

Razaw Salam Rasul, Shazad Shawki Ahmed , Bernstein Polynomial Approximation for Fredholm Integro-Differential Equations of Fractional Order with Numerous Constant Delays , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: مجلد 33 عدد 4 (2025): Vol.33 Issue 4 ( 2025)
Hozan Hilmi, Shabaz Jalil MohammedFaeq, Shwan Swara Fatah, Exact and Approximate Solution of Multi-Higher Order Fractional Differential Equations Via Sawi Transform and Sequential Approximation Method , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: Vol.32 No 1 ( 2024)
Bevreen R. Aliqalawlis, Using Variable Iterative Method to Calculate the Numerical Approximations Solution for Fractional Differential Equations , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: Vol.33 No 1( 2025)
Shazad Shawki Ahmed , Miran B. M. Amin , Shokhan A. Hamasalih, Laplace Adomian Decomposition and Modify Laplace Adomian Decomposition Methods for Solving Linear Volterra Integro-Fractional Differential Equations with Constant Multi-Time Retarded Delay , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: مجلد 27 عدد 5 (2019)
Lavan Sdiq Salih, Shazad Shawki Ahmed, A Bernstein Operational Matrix Approach for Solving Certain Nonlinear Volterra-Fredholm Integro-Differential Equations Involved by Caputo Fractional Derivative , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: Vol.33 ; No. 3 ( 2025)
Hozan M. Ali, Faraidun K. Hamasalh, An Efficient Hermite Polynomial Solution to the Fractional Differential Equations , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: مجلد 33 عدد 4 (2025): Vol.33 Issue 4 ( 2025)
Faraidun K. Hamasalh, Seaman S. Hamasalh, Spline Fractional Polynomial for Computing Fractional Differential Equations , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: مجلد 30 عدد 2 (2022)
Hozan Hilmi, Karwan H.F Jwamer, Existence and Uniqueness Solution of Fractional Order Regge Problem , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: مجلد 30 عدد 2 (2022)
Shokhan A. Hamasalih , Mariwan R. Ahmed, Shazad Shawki Ahmed, Solution Techniques Based on Adomian and Modified Adomian Decomposition for Nonlinear Integro-Fractional Differential Equations of the Volterra-Hammerstein Type , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: مجلد 28 عدد 1 (2020)
Faraidun K. Hamasalh, Mizhda Abbas Headayat, The Numerical Investigations of Non-Polynomial Spline for Solving Fractional Differential Equations , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: مجلد 28 عدد 3 (2020)

يمكنك أيضاً إبدأ بحثاً متقدماً عن المشابهات لهذا المؤلَّف.

الأعمال الأكثر قراءة لنفس المؤلف/المؤلفين

Shazad Shawki Ahmed , Miran B. M. Amin , Shokhan A. Hamasalih, Laplace Adomian Decomposition and Modify Laplace Adomian Decomposition Methods for Solving Linear Volterra Integro-Fractional Differential Equations with Constant Multi-Time Retarded Delay , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: مجلد 27 عدد 5 (2019)
Hozan Hilmi, Shabaz Jalil MohammedFaeq, Shwan Swara Fatah, Exact and Approximate Solution of Multi-Higher Order Fractional Differential Equations Via Sawi Transform and Sequential Approximation Method , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: Vol.32 No 1 ( 2024)
Lavan Sdiq Salih, Shazad Shawki Ahmed, A Bernstein Operational Matrix Approach for Solving Certain Nonlinear Volterra-Fredholm Integro-Differential Equations Involved by Caputo Fractional Derivative , مجلة جامعة بابل - للعلوم الصرفه والتطبيقية: Vol.33 ; No. 3 ( 2025)