Existence and controllability of fractional evolution equation with sectorial operator and impulse

Abstract

This paper deals with the existence and uniqueness of PC-mild solutions for fractional impulsive evolution equation involving nonlocal conditions and sectorial operators. We also study the nonlocal controllability of the control system governed by fractional impulsive evolution equation.

Existence and controllability of fractional evolution inclusions with impulse and sectorial operator

“…In Section 3, we investigate the existence P C−mild solution of nonlocal fractional impulsive problem for abstract evolution inclusion (1). Our fundamental result, Theorem 3.1, extends Theorem 3.1 of [31] and Theorem 3.1 of [37] by discussing the problem in a new case. We study the problem when the function F is upper semicontinuous multifunction.…”

“…Recently,the topic of inclusions of evolution and equations involving sectorial or almost sectorial terms has been extensively studied ( see [2,7,30,31,32,34,35,37]). For instance, Shu et al [31] introduced a dierent concept of mild solutions for (1) when F is a completely continuous single-valued function and A is a sectorial operator with {S α (t) : t ≥ 0} and {T α : t ≥ 0} are compact.…”

“…They determined the dimension for mild solutions set. Zhang et al [37] studied the existence and controllability of (1) when when F is Lipschitz continuous single-valued function and A is a sectorial operator. In Section 3, we investigate the existence P C−mild solution of nonlocal fractional impulsive problem for abstract evolution inclusion (1).…”

Controllability of nonlinear fractional evolution systems in Banach spaces: A survey

“…As we all know, control theory is an interdisciplinary branch of economics, engineering and mathematics that investigates and analyses some dynamical behaviors of various systems [78,92,115,130,131]. In addition, control theory of dynamical systems with impulse [7,35,47,74] or time delay [39,48,109,110] have been studied in the last decates.…”

Existência de soluções suaves "e"-positivas de equações diferenciais fracionárias de evolução impulsivas

“…Além disso, muitas questões ainda precisam ser respondidas, o que enriquecerá a teoria em geral. Aqui, destacamos alguns trabalhos relevantes na teoria das equações diferenciais fracionárias envolvendo operadores setoriais e quase setoriais [17,20,73,76,78,79]. Evidentemente, é notável a importância das equações diferenciais fracionárias tanto no âmbito teórico quanto no de aplicação.…”