Effects of the ARA transform method for time fractional problems

Abstract

The aim of this study is to establish the solutions of time fractional mathematical problems with the aid of new integral transforms called the ARA transform. The fractional derivative is taken in the sense of Liouville-Caputo derivative. The fractional partial differential equations are reduced into ordinary differential equations. Later solving this fractional equation and applying inverse the ARA transform, the solution is acquired. The implementation of this transform for fractional differential equations is very similar to the implementation of the Laplace transform. However, the ARA transform allows us to take the integral transform of some functions for which we can not take the Laplace transform. The illustrated examples justify that the implementation and efficiency of this method are better than any other integral transforms to tackle time fractional differential equations (TFDEs).

Keywords

• liouville-caputo fractional derivative
• time fractional partial differential equation
• ara integral transform