Solutions for Linear Fractional Differential Equations with Multiple Constraints Using Fractional B-Poly Bases
Year: 2025
Type: article
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.
Source: Mathematics
DOI: 10.3390/math13193084
Institution: The University of Texas Rio Grande Valley
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4414511827