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Existence of solutions and approximate controllability of fractional nonlocal neutral impulsive stochastic differential equations of order \(1<q<2\) with infinite delay and Poisson jumps. (English) Zbl 1370.34136

Summary: In this paper, we study the existence of mild solutions and the approximate controllability of nonlinear fractional nonlocal neutral impulsive stochastic differential equations of order \(1<q<2\) with infinite delay and Poisson jumps in which the initial value belong to the abstract phase space \(C_h\). The existence of mild solutions is derived with the help of Sadovskii’s fixed point theorem. The approximate controllability of the nonlinear fractional nonlocal neutral impulsive stochastic differential systems of order \(1<q<2\) with infinite delay and Poisson jumps is discussed under the assumption that the corresponding linear system is approximately controllable. Moreover, the approximate controllability of the above control system is established by using Lebesgue dominated convergence theorem. An example is provided to illustrate the theory.

MSC:

34K37 Functional-differential equations with fractional derivatives
34K50 Stochastic functional-differential equations
93B05 Controllability
34K30 Functional-differential equations in abstract spaces
34K45 Functional-differential equations with impulses
34K35 Control problems for functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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