The fuzzy D'Alembert solutions of the fuzzy wave equation under generalized differentiability

Abstract

In this paper, a one-dimensional homogeneous fuzzy wave equation is solved with an analytical procedure using the fuzzy D’Alembert method by considering the generalized differentiability. Then, some definitions related to fuzzy numbers, theorems, and used lemmas are given. Additionally, the physical interpretation and dependency domain of fuzzy wave solutions are investigated by providing examples, where the fuzzy wave solutions are in the form of fuzzy standing, traveling, and recursive waves.

Keywords

• generalized hukuhara differentiability
• fuzzy partial differential equation
• fuzzy wave equation
• fuzzy d'alembert method