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In this paper, the existence of solutions for differential inclusions of fractional order q∈(1,2]Open image in new window with nonlocal strip conditions is investigated. Our study includes two cases: (i) the multivalued map involved in the problem is not necessarily convex valued, (ii) the multivalued map consists of non-convex values. We combine the nonlinear alternative of Leray-Schauder type coupled with the selection theorem of Bressan and Colombo to establish the first result, while the second result relies on Wegrzyk’s fixed point theorem for generalized contractions.

Some existence results for differential inclusions of fractional order with nonlocal strip conditions