Antiperiodic fractional differential inclusions in Banach spaces with deviating argument influences

M. Benyoub, M. Khuddush

We investigate a boundary value problem for a semilinear differential inclusion involving the Riemann-Liouville fractional derivative with a deviating coefficient in a Banach space. The problem features a linear part that generates a bounded C0-semigroup and a nonlinear, multivalued mapping dependent on both time and the function’s prehistory. With an antiperiodic boundary condition, we address this problem using fractional calculus, Mittag-Leffler functions, and topological methods. By reducing the problem to a fixed-point analysis of a multivalued integral operator in a weighted continuous function space, we establish the existence of solutions via a generalized Sadovskii-type fixed point theorem, proving the operator’s condensing properties with respect to a vector measure of noncompactness 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(2) (2025), pp. 133-147