Invoking the concept of \(\alpha \) -dense curves, we develop a new fixed point approach for multi-valued mappings which works under more general conditions than Darbo multi-valued fixed point theorem and its generalizations. We prove some generalizations of Krasnosielskii’s type fixed point theorems and we establish nonlinear alternatives of Leray-Schauder’s type for multi-valued mappings. This theory is then applied to investigate general existence principles of nonlinear hybrid fractional integral inclusions in abstract Banach spaces. Our results extend and generalize a number of earlier works.
