Abstract
•A fractal transport model is formulated with the definition of a fractional derivative of Caputo–Fabrizio.•A finite difference scheme combined with the Legendre-spectral approach is suggested for the fractal transport model.•The error calculation of the new procedure is calculated on the basis of the theoretical foundation of the novel technique.•This equation is an important fractal model for heat diffusion and ocean acoustic propagation.
This paper proposes a finite difference-spectral method toa mobile/immobile fractal transport model formulated with the concept of a fractional derivative of Caputo–Fabrizio. A finite difference scheme is used in temporal space to achieve a semi-discrete configuration, whereas a Legendre-spectral approach proposes for spatial discretization. The error calculation of the new procedure is calculated based on the theoretical foundation of the current technique. Finally, a variety of numerical examples are presented to determine the feasibility and applicability of the suggested method in terms of convergence ratio and accuracy.