Solutions of Fractional Differential Inclusions and Stationary Points of Intuitionistic Fuzzy-Set-Valued Maps

One of the tools for building new fixed-point results is the use of symmetry in the distance functions. The symmetric property of metrics is particularly useful in constructing contractive inequalities for analyzing different models of practical consequences. A lot of important invariant point results of crisp mappings have been improved by using the symmetry of metrics. However, more than a handful of fixed-point theorems in symmetric spaces are yet to be investigated in fuzzy versions. In accordance with the aforementioned orientation, the idea of Presic-type intuitionistic fuzzy stationary point results is introduced in this study within a space endowed with a symmetrical structure. The stability of intuitionistic fuzzy fixed-point problems and the associated new concepts are proposed herein to complement their corresponding concepts related to multi-valued and single-valued mappings. In the instance where the intuitionistic fuzzy-set-valued map is reduced to its crisp counterparts, our results complement and generalize a few well-known fixed-point theorems with symmetric structure, including the main results of Banach, Ciric, Presic, Rhoades, and some others in the comparable literature. A significant number of consequences of our results in the set-up of fuzzy-set- and crisp-set-valued as well as point-to-point-valued mappings are emphasized and discussed. One of our findings is utilized to assess situations from the perspective of an application for the existence of solutions to non-convex fractional differential inclusions involving Caputo fractional derivatives with nonlocal boundary conditions. Some nontrivial examples are constructed to support the assertions and usability of our main ideas.

Automated summary

This study introduces the idea of Presic-type intuitionistic fuzzy stationary point results within a space endowed with a symmetrical structure. The stability of intuitionistic fuzzy fixed-point problems and the associated new concepts are proposed to complement their corresponding concepts related to multi-valued and single-valued mappings. Various consequences of our results in different types of mappings are emphasized and discussed.