A Study on the Existence and Local Attractivity of Solutions to Fractional Order Nonlinear Random Integral Equations Via Fixed Point Theory

In this work, we examine whether a class of fractional order nonlinear random integral equations defined on the set of non-negative real numbers have a random solution and whether such solutions are locally attractive. In addition to appropriate Caratheodory conditions on the random operators involved, the analysis is performed under nonlinear contraction conditions. Using a Krasnoselskii’s fixed point theorem, we rigorously prove the existence of a random solution and investigate their local attractivity, in the sense that every solution starting sufficiently close to it converges asymptotically to the random solution after introducing a set of structural assumptions on the nonlinear random operators. To demonstrate the application of the suggested framework and to validate the theoretical results, specific example is provided. The obtained results could be helpful for modeling and analyzing fractional order systems that arise in uncertain biological and engineering applications.