Existence of mild solutions of some semilinear neutral fractional functional evolution equations with infinite delay

Extremal solutions of Cauchy problems for abstract fractional differential equations

“…For more details, one can see the monographs of Diethelm [8], Kilbas et al [12], Lakshmikantham et al [13], Miller and Ross [18], Podlubny [24] and Tarasov [25]. Moreover, fractional differential equations (inclusions) and optimal controls in Banach spaces are studied by Balachandran et al [2,3], Benchohra et al [4,5], N'Guérékata [21,22], Mophou and N'Guérékata [19], Wang et al [26,27] and Zhou et al [28][29][30] and etc.…”

Solutions to fractional functional differential equations with nonlocal conditions

“…The existence of mild solution to the fractional semilinear differential equation with nonlocal condition is established by Mophou and N'Guerekata [16]. While in their subsequent work [17], they dealt with the existence of solution to the semilinear neutral fractional equation with infinite delay. The maximum regularity of fractional evolution equation in Hilbert space has been studied by Bazhlekova [4].…”

On nonlocal problems for fractional differential equations in Banach spaces

“…For more details, one can see the monographs of Kilbas et al [6], Lakshmikantham et al [7], Miller and Ross [8], Podlubny [12]. Very recently, fractional differential equations and optimal controls in Banach spaces are studied by Balachandran et al [3,4], N'Guérékata [9,10], Mophou and N'Guérékata [11], Wang et al [13][14][15][16][17][18][19][20], Zhou et al [22][23][24] and etc.…”