A class of BVPS for first order impulsive integro-differential equations

Feedback control for fractional impulsive evolution systems

“…Impulsive differential equations have become more and more important in various applications, such as control, physics, chemistry, population dynamics, aeronautics and engineering. For more details, we refer to [1][2][3]7,11,13,[15][16][17][18][19][20][21]26,27]. D = {t i ∈ (0, T ), i = 1, 2, .…”

A new comparison principle and its application to nonlinear impulsive functional integro-differential equations

“…Boundary value problems (BVP) of differential equations have been investigated for many years. Now, nonlinear boundary conditions have drawn much attention, there exist many articles dealing with the problem for different kinds of boundary value conditions such as multi-point, integral boundary condition, and other conditions (see [25][26][27][28][29][30][31][32][33][34][35]). On the other hand, deviated arguments also play an important role in nonlinear analysis.…”

Mild solution of semilinear impulsive integro-differential evolution equation in Banach spaces

“…Impulsive differential equations arise naturally from a wide variety of applications, such as spacecraft control, electrical engineering, medicine biology, echoing, and so on. For more detail on this theory and its applications, we refer to and references therein.…”

“…Semilinear impulsive evolution equations as an important branch of modern mathematics and applied mathematics have been studied by many authors (see and references therein). When A = θ , the corresponding semigroup G ( t )= I , then the impulsive evolution equation becomes the following first‐order impulsive integro‐differential equations in Banach space E : The existence of solutions of the previous problem and its special and related cases have been studied under several kinds of conditions by many authors, for example, .…”