Existence of mild solutions for fractional impulsive neutral evolution equations with nonlocal conditions

Abstract

In this paper, by using the fractional power of an operator and some fixed point theorems, we study the existence of mild solutions for the nonlocal problem of Caputo fractional impulsive neutral evolution equations in Banach spaces. In the end, an example is given to illustrate the applications of the abstract results. MSC: 34K45; 35F25

Approximations of Solutions for an Impulsive Fractional Differential Equation with a Deviated Argument

“…Since t 0 is arbitrary, we deduce that x satisfies the integral Eq. (17). Now, we shall show the uniqueness of the solution to Eq.…”

“…Now, we shall show the uniqueness of the solution to Eq. (17). Let x 1 and x 2 be the two solutions of the (17).…”

“…Such process is investigated in various fields such as biology, physics, control theory, population dynamics, economics, chemical technology, medicine and so on. For the study for impulsive differential equation, we refer to monograph [10,11], and papers [12][13][14][15][16][17][18][19][20][21][22][23] and references given therein.…”

A study on the mild solution of impulsive fractional evolution equations

“…In particular, impulsive fractional evolution equations recently received considerable attention in the literature. The existence, uniqueness and other properties of the mild solutions to impulsive fractional evolution equations have been investigated in many works [5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, the form of solutions to impulsive fractional evolution equations was studied [1][2][3].…”

“…The second type of solution is obtained by taking integrals over [0, t], given by [2,3,[13][14][15][16][17]…”