Abstract
This paper studies a new class of fractional differential inclusions involving two Caputo fractional derivatives of different orders and a Riemann-Liouville type integral nonlinearity, supplemented with a combination of fixed and nonlocal (dual) anti-periodic boundary conditions. The existence results for the given problem are obtained for convex and non-convex cases of the multi-valued map by applying the standard tools of the fixed point theory. Examples illustrating the obtained results are presented.