A study on the mild solution of impulsive fractional evolution equations

Cauchy problem for fractional non-autonomous evolution equations

“…Particularly, as the fractional order semilinear evolution equations are abstract formulations for many problems arising in engineering, physics, chemistry and economy, the theory of fractional evolution equations has attracted increasing attention in recent years and it has developed into an important branch of fractional calculus and fractional differential equations. For more details about fractional calculus and fractional evolution equations, we refer to [1], [3], [5], [6], [9], [10], [12], [13], [18], [19], [22], [26], [31], [32], [33], [34], [35], [36], [37], [38] and the references therein.…”

The existence and Hyers–Ulam stability of solution for an impulsive Riemann–Liouville fractional neutral functional stochastic differential equation with infinite delay of order 1 < β < 2 $1<\beta<2$

“…However, because of disturbance, the behaviors of many real-word systems are not a settled process. Thus, it is crucial to study stochastic differential functions with impulse [2]. A variety of results on the theory of Caputo fractional functional stochastic equations and the Hyers-Ulam stability [3][4][5][6][7][8] of such function have been obtained.…”

Existence results for fractional order impulsive functional differential equations with multiple delays

“…Some researchers have studied fractional order impulsive differential equations and discussed the existence solution of nonlinear functional differential equations with multiple delays [11,12]. Many authors have investigated the existence solutions of fractional function equations with impulse [13][14][15][16][17][18]. However, there are few studies on the existence of fractional order impulsive functional differential equations multi-delays.…”