Sufficient conditions on existence of solution for nonlinear fractional iterative integral equation

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Authors
Faten H. M. Damag
 Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia.
Adem Kilicman
 Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia.
Abstract
In this article, we study nonlinear quadratic iterative integral equations and establish sufficient conditions for the existence
of Volterra solutions for fractional iterative integral equations and solvency in Banach space and \(C_{\ell,\beta}\). In the present work we
use the principle of contraction, Schaefer’s fixed point theorem and the nonexpansive operator method as essential tools. In
this study we consider RiemannLiouville differential operator and prove some related theorems, further provide an example as
an application.
Keywords
 Fractional integral equation
 existence of solution
 Schaefer’s fixed point theorem
 nonexpansive operator.
MSC
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