In this paper, we study the existence, uniqueness, and controllability results for a class of neutral stochastic delay partial differential equations (NSDPDEs for short) driven by a standard Brownian motion and an fBm in the abstract form
Recently, Boufoussi and Hajji in  considered the existence and uniqueness problems of a class of neutral stochastic delay differential equations; that is, B [equivalent to] 0 and g [equivalent to] 0 in (1) by means of the Banach fixed point theory.
On the other hand, the population systems may suffer sudden environmental perturbations, that is, some jump type stochastic perturbations, for example, earthquakes, hurricanes, and epidemics.
In this paper, we consider a stochastic competitive system with distributed delay and general Levy jumps.
The concept of stochastic differential equations was introduced for the first time in 1902 by Gibbs when he studied the integral of Hamilton-Jacobi differential equations to conserve systems in statistical mechanics with random initial states .
The following theorem presents the conditions under Ito stochastic equation (1) admits the solution and it is singular and they all these aspects are presented in the following theorem :
semiflow on [OMEGA] is a random field [phi]: [R.sub.+] X [OMEGA] [right arrow] [OMEGA] such that
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In this paper, we give a Caratheodory  successive approximation for the solution (whenever we have its pathwise uniqueness) of a d-dimensional stochastic
differential equation where the coefficients are not necessarily continuous.