An Existence Result in <i>α</i>-norm for Impulsive Functional Differential Equations with Variable Times

The dynamics of evolving processes is often subjected to abrupt changes such as shocks, harvesting, and natural disasters. Often these short-term perturbations are treated having acted instantaneously or in the form “impulses.” In fact, there many phenomena real world, which during their development external influences. Their duration negligible compared with total studied processes. Impulsive differential equations take an important place some area that physics, chemical technology, population dynamics, biotechnology, economics. study relatively less developed due difficulties created by state-dependent impulses. case impulses at variable times, a “beating phenomenon” may occur, say, solution equation hit given barrier several times (including infinitely times). this work, we existence solutions for partial impulsive functional Banach spaces using fractional power closed operators theory. We suppose undelayed part admits analytic semigroup. delayed assumed be Lipschitz. use Schaefer fixed-point Theorem prove first order impulse α-norm.