Differential inclusions of arbitrary fractional order with anti-periodic conditions in Banach spaces

In this paper, we establish various existence results of solutions for fractional differential equations and inclusions of arbitrary order q ∈ (m − 1, m), where m is an arbitrary natural number greater than or equal to two, in infinite dimensional Banach spaces, and involving the Caputo derivative in the generalized sense (via the Liouville–Riemann sense). We study the existence of solutions under both convexity and nonconvexity conditions on the multivalued side. Some examples of fractional differential inclusions on lattices are given to illustrate the obtained abstract results.