A generalized neutral-type inclusion problem in the frame of the generalized Caputo fractional derivatives.

In this paper, we study the existence of solutions for a generalized sequential Caputo-type fractional neutral differential inclusion with generalized integral conditions. The used fractional operator has the generalized kernel in the format of (ϑ (t) − ϑ (s)) along with differential operator 1 ϑ ′ (t) d d t . We obtain existence results for two cases of convex-valued and nonconvex-valued multifunctions in two separated sections. We derive our findings by means of the fixed point principles in the context of the set-valued analysis. We give two suitable examples to validate the theoretical results. [ABSTRACT FROM AUTHOR]