Solvability of Nonlinear Volterra-Hammerstein type Fractional Integral Equations in Orlicz Space

Solvability of Nonlinear Volterra-Hammerstein type...

Abstract

In this paper, we are focused on analyzing new analytical properties of $g$-fractional type operators, such as continuity, boundedness and monotonicity in Orlicz spaces $L_\varphi $. Using these properties, along with Darbo’s Fixed-Point theorem and the measure of noncompactness, we investigate the existence and uniqueness of solutions to a nonlinear fractional integral equation in $L_\varphi $. The $ g$-fractional operators being investigated for the first time in the space $L_\varphi .$  Here we generalizes various fractional operators and encompassing and unifying the results of many specific cases of classical and quadratic fractional issues explored in the previous literature. Lastly, we provide some examples to illustrate our main results.