ahmed mahmoud youssef ali
Asst. Lecturer
Approximations for Fractional Derivatives and Fractional Integrals Using Padé Approximation
Journal of Applied Mathematics • 2025
Publication Information
Authors
Ahmed M. Youssef, Tamer M. Rageh, Aisha F. Fareed, and M. S. Abdelwahed
Keywords
fractional calculus; fractional derivatives; fractional integral; Padé approximation; Taylor approximation
Journal
Journal of Applied Mathematics
Publisher
wiley
Volume
2025
Issue
1
Pages
10
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
This paper tackles the persistent challenge of slow convergence and numerical instability in the fractional calculus when applied to
power series–representable functions f(x)=∑_(i=0)^(∞ )▒〖 c_i x〗^i , limitations that compromise accuracy in scientific applications. A novel
reformulation of fractional derivatives and integrals is achieved by applying Padé approximation to conventional power series
solutions, replacing them with optimized rational functions. The modified operators demonstrate significantly improved accuracy and enhanced convergence properties compared to established methods.This approach enables more reliable fractional modeling in physics and engineering domains where traditional operators fail. The work constitutes the first
systematic integration(differentiation) of Padé approximation into the foundational definition of fractional operators, overcoming convergence barriers inherent in prior series-based techniques.
power series–representable functions f(x)=∑_(i=0)^(∞ )▒〖 c_i x〗^i , limitations that compromise accuracy in scientific applications. A novel
reformulation of fractional derivatives and integrals is achieved by applying Padé approximation to conventional power series
solutions, replacing them with optimized rational functions. The modified operators demonstrate significantly improved accuracy and enhanced convergence properties compared to established methods.This approach enables more reliable fractional modeling in physics and engineering domains where traditional operators fail. The work constitutes the first
systematic integration(differentiation) of Padé approximation into the foundational definition of fractional operators, overcoming convergence barriers inherent in prior series-based techniques.