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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    $( \vartheta (t)-\vartheta (s)) $  ( ϑ ( t ) − ϑ ( s ) ) along with differential operator    $\frac{1}{\vartheta '(t)}\,\frac{\mathrm{d}}{\mathrm{d}t}$  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.

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