On solution of Diffusion Equation using Conformable Laplace Transform

TL;DR

This paper extends classical Laplace transform properties to conformable fractional transforms and uses them to analytically solve diffusion equations with initial-boundary conditions.

Contribution

It develops the inversion and convolution theorems for conformable fractional Laplace transforms and applies these to solve diffusion equations analytically.

Findings

Extended classical Laplace properties to conformable fractional transforms

Derived analytical solutions for diffusion equations using conformable Laplace transform

Established foundational theorems for conformable fractional Laplace transforms

Abstract

The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using these properties, we found analytical solutions to the initial-boundary value problems of the diffusion equation.