The existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay

Optimal controls for a class of impulsive fractional differential equations with nonlocal conditions

“…The existence of fractional differential equation has received attention of many authors (see [6][7][8][9]). The monographs of Bazhlekova [10], Guo et al [11], Miller et al [12], Podlubny [13], and the papers [14][15][16] can provide more details and references about the theory and application of fractional differential equations.…”

On the concept of general solution for impulsive differential equations of fractional-order q ∈(1, 2)

“…The subject of fractional differential equations is gaining much attention. For detail, see [1][2][3][4][5][6][7][8][9][10][11][12] and the references therein.…”

Approximate Controllability of Semilinear Fractional Stochastic Dynamic Systems with Nonlocal Conditions in Hilbert Spaces

“…Recently, there has been a significant development in the existence and uniqueness of solutions to fractional differential equations with nonlocal conditions. Zhang and Huang [34] studied the existence and uniqueness of mild solutions for impulsive fractional equations with nonlocal conditions and infinite delay. Shu and Wang [29] proved the existence of mild solutions for fractional differential equations with nonlocal conditions of order 1 < α < 2 and, very recently, Ahmed [2] investigated the existence of mild solutions to semilinear neutral fractional differential equations involving nonlocal initial conditions.…”