Three-Dimensional Fourth-Order Time-Fractional Parabolic Partial Differential Equations and Their Analytical Solution

Abstract

In this study, the fractional reduced differential transform method (FRDTM) is employed to solve three-dimensional fourth-order time-fractional parabolic partial differential equations with variable coefficients. The fractional derivative used in this study is in the Caputo sense. A few important lemmas which are essential to solve the problems using the proposed method are proved. The novelty of this method is that it uses appropriate initial conditions and finds the solution to the problems without any discretization, linearization, perturbation, or any restrictive assumptions. Two numerical examples are considered in order to validate the efficiency and reliability of the method. Furthermore, the FRDTM solution when α = 1 is compared with other analytical methods available in the existing literature. Computational results are shown in tables and graphs. The obtained results revealed that the method is capable and simple to solve fractional partial differential equations. The software used for the calculations in this study is Mathematica 7.