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.

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.

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 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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