In this paper, we consider generalized {\alpha-\psi}-Geraghty contractive type mappings and investigate the existence and uniqueness of a fixed point for mappings involving such contractions. In particular, we extend, improve and generalize some earlier results in the literature on this topic. An application concerning the existence of an integral equation is also considered to illustrate the novelty of the main result.

Abstract. In this paper, we introduce the notion of generalized α − ψ-Geraghty multivalued mappings and investigate the existence of a fixed point of such multivalued mappings. We present a concrete example and an application on integral equations illustrating the obtained results.

In this paper, we investigate the existence of positive solutions for the new class of boundary value problems via ψ-Hilfer fractional differential equations. For our purpose, we use the $\alpha -\psi $ α − ψ Geraghty-type contraction in the framework of the b-metric space. We give an example illustrating the validity of the proved results.

In this article, using by α-admissible and α qs p-admissible mappings, solutions of some fractional differential equations are investigated in quasi-b-metric and b-metric-like spaces.

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In this paper, we introduce the concept of generalized [Formula: see text]-Suzuki-contractions in the context of quasi [Formula: see text]-metric-like spaces and we establish some related fixed point theorems. As consequences, we obtain some known fixed point results in the literature. Some concrete examples are also provided illustrating the obtained results.

By using fixed point results of mixed monotone operators on cones and the concept of ?-concavity, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Some concrete examples are also provided illustrating the obtained results.

Using some fixed point theorems for contractive mappings, including α-γ-Geraghty type contraction, α-type F-contraction, and some other contractions in F-metric space, this research intends to investigate the existence of solutions for some Atangana-Baleanu fractional differential equations in the Caputo sense.