SOLVING PARTIAL FRACTIONAL DIFFERENTIAL EQUATIONS USING THE $\mathcal{L}_A $-TRANSFORM

Abstract

In this article, the authors introduce the [Formula: see text]-transform and derive the complex inversion formula and a convolution theorem for the transform. Furthermore, the fundamental solution of the Cauchy type fractional diffusion equation on fractals is given by means of the [Formula: see text]-transform in terms of the Wright functions. Also, the Cauchy fractional disturbance equation with continuous or discrete distribution of time fractional derivative is introduced and by using the [Formula: see text]-transform, its solution is expressed in terms of the Laplace type integral.