Solution of fractional integral equations via fixed point results

Abstract

In this paper, we introduce two new concepts of F-contraction, called dual F^{*}-weak contraction and triple F^{*}-weak contraction, which generalize the existing contractions in the sense of Wardowski, Jleli and Samet as well as Skof. These new generalizations embed their roots in the aim devoted to extending the generalized Banach contraction conjuncture to the class of F-contraction type mappings with the use of multiple F-type functions. Furthermore, we establish the existence of a unique fixed point for such contractions under certain conditions. Fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates that can be expressed as functions of one independent variable. We apply our main result to weaken certain conditions on the fractional integral equations. Finally, we discuss the significance of our obtained results in comparison with certain renowned ones in the literature.