On Dirichlet Problem of Time-Fractional Advection-Diffusion Equation

Abstract

The significant motivation behind this research article is to utilize a technique depending upon acertain variant of the integral transform (Fourier and Laplace) to investigate the basic solution for theDirichlet problem with constant boundary conditions. The time-fractional derivative one-dimensional,the equation of advection-diffusion and the Liouville-Caputo fractional derivative in a line fragment areintroduced. We also illustrate the results using graphical representations