In this paper, we introduce a new class of contractive mappings in fuzzy metric spaces and we present some fixed point results for this class of maps.

Generalized Geraghty type fuzzy mappings on complete metric spaces are introduced and a fixed point theorem that generalizes some recent comparable results for fuzzy mappings in contemporary literature is obtained.Example is provided to show the validity of obtained results over comparable classical results for fuzzy mappings in fixed point theory. As an application, existence of coincidence fuzzy points and common fixed fuzzy points for hybrid pair of single valued self mapping and a fuzzy mapping is also established.

In the present paper, we introduce the concept of generalized multivalued F -contraction mappings and give a fixed point result, which is a proper generalization of some multivalued fixed point theorems including Nadler's.

In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of complete generalized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergent matrix technique with Schauder fixed point principle of vector valued operators in semilinear Banach spaces. Some computational examples are represented to demonstrate our theoretical results.