Fuzzy analysis of 2-D wave equation through Hukuhara differentiability coupled with AOS technique

Abstract

The research article in hand provides a new mechanism that deals with the investigation of the triangular analytical fuzzy solutions (TAFS) of the two-dimensional fuzzy fractional order wave equation (2-D FFWE) through the Hukuhara conformable fractional derivative (HCFD) along with the concept of [gH] and [gH−p] differentiability. The mechanism consists of a fuzzy traveling wave method coupled with additive operating splitting (AOS). The procedure for the aforesaid mechanism starts with the extension of the HCFD to the fuzzy conformable fractional derivative (FCFD). Furthermore, some properties of FCFD that play a vital role in this study like, ([i−gH],[ii−gH],[i−p],[ii−p])-differentiability, switching point, fuzzy chain rule, and traveling wave method are discussed in detail. Further, fuzzy traveling wave method coupled with the procedure of the additive operating splitting (AOS) method is adopted to investigate the triangular analytical fuzzy solution of the Two-dimensional fuzzy wave equation (2-D FWE). Finally, some examples are provided that support our arguments.

Keywords

• Fuzzy wave equation
• Hukuhara conformable fractional derivative
• ([i−gH],[ii−gH],[i−p],i−p])-differentiability
• Switching point
• Fuzzy chain rule
• Traveling wave method