Nonlocal Cauchy problem for fractional stochastic evolution equations in Hilbert spaces

Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

“…(ii) When ] = 1, the fractional stochastic equation (1) simplifies to the classical Caputo fractional equation which has been discussed by Chen and Li [25]. In this case, 1, ( ) = ( ), 0 ≤ ≤ , where ( ) is defined in [25].…”

“…Thus, it is of great importance to design stochastic effects in the study of fractional-order 2 Discrete Dynamics in Nature and Society dynamical systems. Chen and Li [25] reported the existence results of fractional stochastic integrodifferential equations with nonlocal initial conditions in Hilbert space. Wang [26] investigated the existence results of fractional stochastic differential equations by using Picard type approximation.…”

Existence of a mild solution for an impulsive nonlocal non-autonomous neutral functional differential equation

“…In [8], author has shown the controllability of a system of impulsive semilinear non-autonomous differential equations via Rothe's type fixed-point theorem. For more details and study on such differential equation, we refer to the monographs [9,10] and papers [11][12][13][14][15][16][17][18][19][20] and reference cited therein.…”

“…In [16], authors have considered an impulsive stochastic functional integro-differential inclusions with nonlocal conditions in a Hilbert space and provided existence results for mild solution by using approximation technique and BohnenblustKarlins fixed point theorem. In [17], authors have concerned with the existence of α-mild solutions for a fractional stochastic integro-differential equations with nonlocal initial conditions in a real separable Hilbert space by using an approximation technique. For more details, we refer to papers [11,[14][15][16][17][18][19][20]24,26,28] and references given therein.…”

On the initial value problem of fractional stochastic evolution equations in Hilbert spaces

“…Chen and Li [8] investigated the existence of α-mild solutions for a class of fractional stochastic integro-differential evolution equations with nonlocal initial conditions in a real separable Hilbert space by using Schauder fixed point theorem and approximating techniques. Cui and Yan [9] discussed the existence of mild solutions for a class of fractional neutral stochastic integrodifferential equations with infinite delay in Hilbert spaces by means of Sadovskii's fixed point theorem.…”