Computational Study of Constant and Variable Coefficients Time-Fractional PDEs via Reproducing Kernel Hilbert Space Method

Authored by: Ali Akgül , Nourhane Attia

Handbook of Fractional Calculus for Engineering and Science

Print publication date:  February  2022
Online publication date:  February  2022

Print ISBN: 9781032047799
eBook ISBN: 9781003263517
Adobe ISBN:




In this chapter, a reproducing kernel Hilbert space method (RKHSM) is proposed for studying time-fractional PDEs. Specifically, the RKHSM is applied for time-fractional heat-like and Navier-Stokes equations when the equations’ coefficients vary between constants and variables. These equations have significant applications in applied sciences and engineering. The current approach utilizes some important binary reproducing kernel Hilbert (RK) spaces with appropriate RK functions. Error estimations and convergence analysis of the proposed method are discussed. The RKHSM is assessed by testing some illustrative applications which have exact solutions. The results suggest that the RKHSM is a very effective and highly convenient method for solving time-fractional PDEs arising in widespread fields of engineering and applied sciences.

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