SOLVABILITY OF QUADRATIC HADAMARD-TYPE FRACTIONAL INTEGRAL EQUATIONS IN ORLICZ SPACES

Abstract

We demonstrate some properties of Hadamard fractional operators such as boundedness, monotonicity, continuity, and acting conditions in Orlicz spaces $L_{\phi }$. We apply these properties with a proper measure of noncompactness (MNC) to inspect the existence of monotonic solutions of some general, but abstract, form of quadratic Hadamard-type fractional integral equations in $L_{\phi }$. We also discuss the uniqueness of the solution.