An approximate solution to the transient space-fractional diffusion equation: Integral-balance approach, optimization problems and analyzes

Abstract

This paper presents approximate analytical solutions of an initial-boundary value problem of fractional partial differential diffusion equation with spatial Riemann-Liouville fractional derivative. The proposed approximate solutions are based on the concept of a finite penetration depth with the integral-balance method and series expansions of the assumed parabolic profile with undefined exponent. Optimization problems referring to optimal exponents of the assumed parabolic have been developed.