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

In this article, the authors introduce the -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 -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 -transform, its solution is expressed in terms of the Laplace type integral.

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