existence of solution for a fractional differential equation via a new type of (ψ, f)-contraction in b-metric spaces

In this paper, we further develop the notion of cyclic (α, β)-admissible mappings introduced in ([14], s. chandok, k. tas, a. h. ansari, some fixed point results for tac-type contractive mappings, j. function spaces, 2016, article id 1907676, 1–6) and (ψ, f)-contraction mappings introduced in ([34], d. wardowski, solving existence problems via f-contractions, proceedings of the american mathematical society, 146 (4), (2018), 1585–1598), in the framework of b-metric spaces. to achieve this, we introduce the notion of (α, β) − s-admissible mappings and a new class of generalized (ψ, f)-contraction types and establish a common fixed point and fixed point results for these classes of mappings in the framework of complete b-metric spaces. as an application, we establish the existence and uniqueness of the solutions to differential equations in the framework of fractional derivatives involving mittag-leffler kernels via the fixed point technique. the results obtained in this work provide extension as well as substantial generalization and improvement of the fixed point results obtained in [14, 34, 35] and several well-known results on fixed point theory and its applications.