Modified Fourier transform for solving fractional partial differential equations

Abstract

In recent years many physical phenomenons have been successfully modelled using fractional partial differential equations such as in electromagnetics and material sciences. Fractional partial differential equations involve derivative of noninteger order. Many researchers attempted to solve various types of fractional differential equations using various methods. In this paper, the conformable fractional derivative definition introduced by Khalil et.al [4] is used. The fractional derivative using this definition satisfies many properties that the usual derivative has. By applying some similar arguments on Fourier transform for solving partial differential equations, some modifications on the Fourier transform are constructed to handle the fractional order in a fractional differential equation. The modified Fourier transform which is developed satisfies similar properties with the Fourier transform in the classical sense. The application of the method to solve a fractional differential equation is given as an example.