Methods of Integral Transforms for Solving Integral and Differential Equations of Fractional Order With Applications

Abstract

Problems involving the physical phenomena of time-fractional advection dispersion equation are formulated in the form of partial differential and integral equation of fractional order. The present thesis is mainly concerned with developing the analytical methods used and applied to solve such type of equations. Also, The first Stokes` problem and Rayleigh-Stokes equations and energy equation have been treated and solved . A time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform along with an intermediate step of Mellin transform have been applied to achieve an exact solution in terms of H-function and the complement error function. A number of special cases are also considered. Exact solution of the time-fractional advection-dispersion equation with reaction term has been obtained. The solution is achieved by using Fourier and Laplace transforms to get the formulas of the fundamental solution, which are expressed explicitly in terms of Fox’s