Integral Boundary Value Problem for Intuitionistic Fuzzy Partial Hyperbolic Differential Equations

Abstract

The concept of intuitionistic fuzzy is introduced by Atanassov [5, 8]. It’s a generalization of fuzzy theory introduced by Zadeh [55]. Few works on intuitionistic fuzzy differential equations till date after developing intuitionistic fuzzy set theory [17, 18, 37]. Intuitionistic partial differential equations are very rare, the concept of intuitionistic fuzzy partial differential equations was introduced by S. Melliani and L. S. Chadli in [38]. In this paper, we consider the boundary valued problems for intuitionistic fuzzy partial hyperbolic differential equations with integral boundary conditions. A new complete intuitionistic fuzzy metric space [39] is proposed to investigate the existence and uniqueness of intuitionistic fuzzy solutions for these problems using the theorem of fixed point. Also we have presented an useful procedure to solve intuitionistic fuzzy partial hyperbolic differential equations. Some illustrated examples for our results are given with some numerical simulations for \(\alpha \)-cuts of the intuitionistic fuzzy solutions.