The Initial Value Problem for 2D Time Fractional Beam Equation and Its Exact Solution by Reduced Differential Transform Method

Abstract

The primary goal of this research is to devise a method for obtaining the exact solution of the initial value problem of two dimensional homogeneous and non-homogeneous time fractional beam equation. The reduced and inverse reduced differential transformed functions in two dimensional are defined for solving the initial value problem of two-dimensional time fractional beam equation. Some theorems are stated and proved in solving the above initial value problem. The two-dimensional time fractional beam theory is derived from the convectional beam equation by substituting the fractional derivative for the integer order time derivative in the normal beam equation. The fractional derivative involved here is in sense of Caputo fractional derivatives, which has the benefit that the initial conditions for fractional differential equations adopt the usual form for integer order differential equations.