Abstract
In the present paper, we extend and develop a qualitative analysis for a class of nonlinear fractional inclusion problems subjected to nonlocal integral boundary conditions (nonlocal IBC) under the w-Hilfer operator. Both claims of convex valued and nonconvex valued right-hand sides are investigated. The obtained existence results of the proposed problem are new in the frame of a phi-Hilfer fractional derivative with nonlocal IBC, which are derived via the fixed point theorems (FPT's) for set-valued analysis. Eventually, we give some illustrative examples for the acquired results.