Ass. Lect. ahmed mahmoud youssef ali :: Publications:

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.