Existence results of delay and fractional differential equations via fuzzy weakly contraction mapping principle

Abstract

The purpose of this article is to extend the results derived through former articles with respect to the notion of weak contraction into intuitionistic fuzzy weak contraction in the context of (T,N,∝) -cut set of an intuitionistic fuzzy set. We intend to prove common fixed point theorem for a pair of intuitionistic fuzzy mappings satisfying weakly contractive condition in a complete metric space which generalizes many results existing in the literature. Moreover, concrete results on existence of the solution of a delay differential equation and a system of Riemann-Liouville Cauchy type problems have been derived. In addition, we also present illustrative examples to substantiate the usability of our main result.