On Fuzzy Conformable Double Laplace Transform with Applications to燩artial Differential Equations

Abstract

The Laplace transformation is a very important integral transform, and it is extensively used in solving ordinary differential equations, partial differential equations, and several types of integro-differential equations. Our purpose in this study is to introduce the notion of fuzzy double Laplace transform, fuzzy conformable double Laplace transform (FCDLT). We discuss some basic properties of FCDLT. We obtain the solutions of fuzzy partial differential equations (both one-dimensional and two-dimensional cases) through the double Laplace approach. We demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations.

On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

“…Actually, it is efficient and easy to implement when compared to other analytical methods. Some frequent results in this regards are cited here as [65][66][67]. In this work, we further compare our results with those obtained by the homotopy perturbation method (HPM) by using the Caputo derivative.…”