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 $( \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.

EXISTENCE RESULTS FOR IMPULSIVE SYSTEMS WITH INITIAL NONLOCAL CONDITIONS

We study the existence of solutions for nonlinear first order impulsive systems with nonlocal initial conditions. Our approach relies in the fixed point principles of Schauder and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.

On a New Class of Antiperiodic Fractional Boundary Value Problems

This paper investigates a new class of antiperiodic boundary value problems of higher order fractional differential equations. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Some examples are given to illustrate the results.

Multi-valued mappings and fixed points II

In this paper, some hybrid fixed point principles for the sum of two multi-valued operators in a Banach space are proved and they are further applied to a certain integral inclu- sion of mixed type for proving the existence results under mixed Lipschitz and Carath´eodory conditions.