Open Access

ARTICLE

On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations

Thabet Abdeljawad^1,2, Awais Younus^3,*, Manar A. Alqudah⁴, Usama Atta⁵

1 Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
2 Department of Medical Research, China Medical University, Taichung, 40402, Taiwan
3 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakaryia University, Multan, 60000, Pakistan
4 Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, Riyadh, 11671, Saudi Arabia
5 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakaryia University, Multan, 60000, Pakistan

* Corresponding Author: Awais Younus. Email:

(This article belongs to the Special Issue: Advanced Numerical Methods for Fractional Differential Equations)

Computer Modeling in Engineering & Sciences 2023, 134(3), 2163-2191. https://doi.org/10.32604/cmes.2022.020915

Received 19 December 2021; Accepted 05 May 2022; Issue published 20 September 2022

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.

---