This paper investigates non-fractional operators, a type of nonlocal operator, within the framework of Orlicz spaces. Using inclusions between certain function spaces, we prove the continuity and/or compactness of generalized operators in Orlicz spaces and show that solutions exist for integral equations of fractional order. We also introduce a generalized Hilfer-type derivative and examine the equivalence of differential and integral problems. Finally, we relate these results to the study of compositional p-Laplacian fractional problems involving generalized Hilfer fractional derivatives. Among other things, we prove the existence of solutions to such problems in Orlicz and Orlicz–Sobolev spaces.
Cichoń et al. (Fri,) studied this question.