Impulsive functional delay differential inclusions of fractional order at variable times

Abstract

We are concerned with some sufficient conditions for the existence of solutions of a class of initial value problems for impulsive fractional differential inclusions with functional delay at variable moments.

Existence of solutions for fractional differential inclusions with initial value condition and non-instantaneous impulses

“…In this paper, we are concerned with a kind of ψ-Hilfer fractional order differential inclusions. The addressed system with the fractional order has non-instantaneous impulsive effects, which are quite different from the related references discussed in the literatures [22,24,25,27]. The fractional-order nonlinear differential system studied in the present paper is more generalized and more practical.…”

“…As a consequence, differential inclusions have been the subject of an intensive study of many researchers. Impulsive differential inclusions have also been researched by many experts, and we can see the monograph [4] and papers [21,22,24,25,27]. Also, fractional differential equations have been studied by many researchers.…”

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

“…Due to the superiority and generalizations achieved by fractional-order derivatives, impulsive fractional-order inclusions have also been investigated by some researchers [48][49][50][51]. However, no results on the almost periodic waves of fractional differential inclusions have been reported in the existing literature.…”

Lyapunov Pairs in Semilinear Differential Problems with State-Dependent Impulses

“…All the cited papers deal with fixed moments of impulses, but in fact as well as fixed beforehand the moments of impulses can be chosen in various ways, for instance, randomly, or determined by the state of a system. Existence results for several kind of impulsive differential inclusions with variable times of impulses in a finite dimensional framework are contained in [5,6,16,17,20]. Some interesting results on classical solutions to single-valued impulsive problems in abstract spaces (with state-dependent impulses) can be found in, e.g., [21].…”