TY - JOUR
T1 - Fuzzy analysis of 2-D wave equation through Hukuhara differentiability coupled with AOS technique
AU - Usman, Muhammad
AU - Khan, Hidayat Ullah
AU - Shah, Kamal
AU - Abdalla, Bahaaeldin
AU - Mlaiki, Nabil
AU - Abdeljawad, Thabet
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024/3/30
Y1 - 2024/3/30
N2 - 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.
AB - 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.
KW - ([i−gH],[ii−gH],[i−p],i−p])-differentiability
KW - Additive operating splitting method
KW - Fuzzy chain rule
KW - Fuzzy wave equation
KW - Hukuhara conformable fractional derivative
KW - Switching point
KW - Traveling wave method
UR - http://www.scopus.com/inward/record.url?scp=85187953225&partnerID=8YFLogxK
U2 - 10.1016/j.heliyon.2024.e27719
DO - 10.1016/j.heliyon.2024.e27719
M3 - Article
C2 - 38509950
AN - SCOPUS:85187953225
SN - 2405-8440
VL - 10
JO - Heliyon
JF - Heliyon
IS - 6
M1 - e27719
ER -