We present a new generalization of the Banach contraction principle in the setting of Branciari metric spaces.

We introduce a new concept of generalized metric spaces for which we extend some well-known fixed point results including Banach contraction principle,Ćirić's fixed point theorem, a fixed point result due to Ran and Reurings, and a fixed point result due to Nieto and Rodríguez-López. This new concept of generalized metric spaces recover various topological spaces including standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces. MSC: 54H25; 47H10

The main purpose of this manuscript is to provide a short proof of the metrizability of F-metric spaces introduced by Jleli and Samet in [3, Jleli, M. and Samet, B., On a new generalization of metric spaces, J. Fixed Point Theory Appl. (2018) 20:128].

We discuss the introduced concept of G-metric spaces and the fixed point existing results of contractive mappings defined on such spaces. In particular, we show that the most obtained fixed point theorems on such spaces can be deduced immediately from fixed point theorems on metric or quasi-metric spaces. MSC: 47H10; 11J83

A new fractional derivative with a non-singular kernel involving exponential and trigonometric functions is proposed in this paper. The suggested fractional operator includes as a special case Caputo-Fabrizio fractional derivative. Theoretical and numerical studies of fractional differential equations involving this new concept are presented. Next, some applications to RC-electrical circuits are provided.