Benha University

احمد محمود يوسف على

مدرس مساعد

كلية الهندسة ببنها العلوم الأساسية

Padé Formulation of Fractional Derivatives for Numerical Solution of Fractional Diffusion Equation

Benha Journal of Applied Sciences • 2026
العودة
معلومات البحث
المؤلفون Ahmed M. Youssef1, Tamer M. Rageh1, Aisha F. Fareed, and M. S. abdelwahed
الكلمات المفتاحية Fractional Calculus, Padé Approximation, Taylor Approximation, Fractional Diffusion Equation, Mittag-Leffler function. Fractional Calculus, Padé Approximation, Taylor Approximation, Fractional Diffusion Equation, Mittag-Leffler function. Fractional Calculus, Padé Approximation, Taylor Approximation, Fractional Diffusion Equation, Mittag-Leffler function. Fractional Calculus, Padé Approximation, Taylor Approximation, Fractional Diffusion Equation, Mittag-Leffler function. Fractional Calculus, Padé Approximation, Taylor Approximation, Fractional Diffusion Equation, Mittag-Leffler function.
المجلة العلمية Benha Journal of Applied Sciences
الناشر Benha University
المجلد Not Available
العدد Not Available
الصفحات 12
publication.type Local
رابط البحث Not Available
المواد المرفقة Not Available
الملخص
This study presents a Padé approximation approach for solving time-fractional diffusion equations through rational approximation of power series solutions. The method constructs systematic Padé approximants to represent fractional derivatives without time discretization, maintaining the essential nonlocal character of the operators. Numerical experiments demonstrate accurate agreement with exact Mittag-Leffler function solutions across various fractional orders. The proposed framework provides a flexible and systematic procedure for generating rational approximations of different orders according to the desired level of accuracy. Moreover, the method reduces the computational effort associated with traditional discretization-based techniques while preserving the mathematical properties of the fractional model. Higher-order Padé schemes consistently show better performance than lower-order approximations in terms of solution accuracy and stability. The approach proves particularly effective for problems involving multiple eigenmodes, successfully capturing their interactions. These results establish the method as a reliable computational tool for fractional diffusion problems, offering advantages in both accuracy and efficiency for practical applications in science and engineering.
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