The Diffusive Stresses Arising from A Locally Generalized Advection-Diffusion Process

Abstract

In this paper, one and two-dimensional Cauchy problems based on an advection-diffusion equation withConformable derivative are analysed. This constitutive equation is a natural result of the description of thediffusion coefficient and velocity field with temporally dependent power functions. The main aim of thepresent study is to find the analytical solutions of the revealed one and two-dimensional Cauchy problems.For this purpose, the fractional Laplace and the exponential Fourier integral transformations have beenapplied to obtain the analytical solutions. Correspondingly, the diffusive stresses have been computed byusing some basic principles of classical elasticity theory. Some comparative interpretations have been madewith the Caputo fractional advection-diffusion model to demonstrate the effect of the conformable derivativeon the diffusion.