On Well-Posedness of a General Fractional Integral Equation in Orlicz Spaces

This article has two objectives. The first objective is to utilize Darbo's fixed-point theorem (FPT) and the measure of noncompactness (MNC) technique to study the well-posedness (i.e., the existence and the uniqueness in addition to continuous dependence on the data) of a generalized fractional quadratic integral equation in Orlicz spaces L_ψ. Our second objective is to prove and explain the novel properties of g-fractional operators, such as boundedness, continuity, acting, and monotonicity within L_ψ. As a result of our work, several fractional operators are generalized, unified, and extended, including Riemann-Liouville, Hadamard, and Erdélyi-Kober, as well as related classical and quadratic fractional problems. Our theories are supported by several examples.