Physics & Astronomy Faculty Publications and Presentations
Document Type
Article
Publication Date
9-25-2025
Abstract
This study presents an innovative numerical method for solving linear fractional differential equations (LFDEs) using modified Bernstein polynomial bases. The proposed approach effectively addresses the challenges posed by the nonlocal nature of fractional derivatives, providing a robust framework for handling multiple initial and boundary value constraints. By integrating the LFDEs and approximating the solutions with modified fractional-order Bernstein polynomials, we derive operational matrices to solve the resulting system numerically. The method’s accuracy is validated through several examples, showing excellent agreement between numerical and exact solutions. Comparative analysis with existing data further confirms the reliability of the approach, with absolute errors ranging from 10−18 to 10−4. The results highlight the method’s efficiency and versatility in modeling complex systems governed by fractional dynamics. This work offers a computationally efficient and accurate tool for fractional calculus applications in science and engineering, helping to bridge existing gaps in numerical techniques.
Recommended Citation
Rahman, Md. Habibur, Muhammad I. Bhatti, and Nicholas Dimakis. 2025. "Solutions for Linear Fractional Differential Equations with Multiple Constraints Using Fractional B-Poly Bases" Mathematics 13, no. 19: 3084. https://doi.org/10.3390/math13193084
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Mathematics
DOI
10.3390/math13193084
Comments
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).