Existence Results of a Nonlinear Fractional Integral Equation of Two Variables in the Space of Regulated Functions

Soodabeh Alipour Fatideh, Mahnaz Khanehgir, Reza Allahyari, Mohammad Mehrabinezhad, Hojjatollah Amiri Kayvanloo

Abstract


In the present work, we characterize relatively compact subsets of thespace of regulated functions defined on Davison spaces. Then, we introduce a measureof noncompactness on these spaces. Using the technique of the measure of noncompactnessand a fixed point theorem of Darbo type, we study the existence of solutionsof a nonlinear fractional integral equation of two variables in the space of regulatedfunctions. We also add an illustrative example in verification of our existence results.

Keywords


Darbo’s fixed point theorem, Davison space, Fractional integral equation, Measure of noncompactness, Regulated function

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