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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 Lotka-Volterra (LV) system is an interesting mathematical model because of its significant and wide applications in biological sciences and ecology. A fractional LV model in the Caputo sense is investigated in this paper. Namely, we provide a comparative study of the considered model using Haar wavelet and Adams-Bashforth-Moulton methods. For the first method, the Haar wavelet operational matrix of the fractional order integration is derived and used to solve the fractional LV model. The main characteristic of the operational method is to convert the considered model into an algebraic equation which is easy to solve.To demonstrate the efficiency and accuracy of the proposed methods, some numerical tests are provided. KEYWORDS Adams-Bashforth-Moulton method, fractional LV model, Haar wavelet method, operational matrix MSC CLASSIFICATION 26A33; 34A08; 34A34 Math Meth Appl Sci. 2020;43:5564-5578. wileyonlinelibrary.com/journal/mma

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].