Abstract
In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and merge several existing fixed point theorems that were formulated by linear and nonlinear contractions.
Highlights
Introduction and PreliminariesIn the last few decades, one of the most attractive research topics in nonlinear functional analysis is to solve fractional differential and fractional integral equations that can be reduced properly to standard differential equations and integral equations, respectively
We aim to get a proper solution for Volterra type fractional integral equations by using a hybrid type contraction
We first recall the auxiliary functions that we shall use effectively: Let Ψ be the set of all nondecreasing functions Λ : [0, ∞) → [0, ∞) in a way that (ΛΣ )
Summary
Institut Supérieur d’Informatique et des Techniques de Communication, Université de Sousse, H. China Medical University Hospital, China Medical University, Taichung 40402, Taiwan. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
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