2017
DOI: 10.18514/mmn.2017.2396
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Null controllability of nonlocal Hilfer fractional stochastic differential equations

Abstract: Abstract. In this paper, we study exact null controllability of Hilfer fractional semilinear stochastic differential equations in Hilbert spaces. By using fractional calculus and fixed point approach, sufficient conditions of exact null controllability for such fractional systems are established. An example is given to show the application of our results.2010 Mathematics Subject Classification: 26A33; 93B05

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Cited by 37 publications
(5 citation statements)
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“…The periodic averaging method for impulsive conformable fractional stochastic differential equations with Poisson jumps are discussed in [22] by Ahmed. For some recent works on Hilfer fractional order stochastic differential systems, we refer to [23][24][25][26]. In [27], Ahmed and Zhu investigated the averaging principle for the following Hilfer fractional stochastic delay differential equation with Poisson jumps in the sense of mean square…”
Section: Introductionmentioning
confidence: 99%
“…The periodic averaging method for impulsive conformable fractional stochastic differential equations with Poisson jumps are discussed in [22] by Ahmed. For some recent works on Hilfer fractional order stochastic differential systems, we refer to [23][24][25][26]. In [27], Ahmed and Zhu investigated the averaging principle for the following Hilfer fractional stochastic delay differential equation with Poisson jumps in the sense of mean square…”
Section: Introductionmentioning
confidence: 99%
“…Controllability is one of the fundamental notions of modern control theory, which enables one to steer the control system from an arbitrary initial state to an arbitrary final state using the set of admissible controls where initial and final state may vary over the entire space. The problem of controllability of nonlinear systems represented by fractional differential equations has been extensively studied by several authors; see, for example, [1,9,10,25] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, fractional differential equations have been considered greatly by research community in various aspects due to its salient features for real world problems (see [1][2][3][4][5][6][7]). Controllability problems for different kinds of dynamical systems have been studied by several authors (see [8][9][10][11][12][13][14][15]) and references therein. Thus, the dynamical systems must be treated by the weaker concept of controllability, namely approximate controllability (see [16][17][18][19][20][21]).…”
Section: Introductionmentioning
confidence: 99%