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

Abstract

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

Keywords

• ϑ-Caputo fractional derivatives
• Fixed point
• Fractional differential inclusion
• Generalized Caputo derivative