Approximate Controllability via Resolvent Operators of Sobolev-Type Fractional Stochastic Integrodifferential Equations with Fractional Brownian Motion and Poisson Jumps
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Using fractional calculus, stochastic analysis theory, and fixed point theorems with the properties of analytic \(\alpha \)-resolvent operators, sufficient conditions for approximate controllability of Sobolev-type fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps are established. Finally, an example is given to illustrate the obtained results.
KeywordsFractional Brownian motion Poisson jumps Sobolev-type fractional stochastic integrodifferential equations Approximate controllability Resolvent operators
Mathematics Subject Classification60H15 34A08 60G22 93B05
I would like to thank the referees and the editor for their important comments and suggestions, which have significantly improved the paper.
- 9.Sathya, R., Balachandran, K.: Controllability of Sobolev-Type neutral stochastic mixed integrodifferential systems. European journal of mathematicall sciences 1, 68–87 (2012)Google Scholar
- 13.Mabel Lizzy, R., Balachandran, K., Suvinthra, M.: Controllability of nonlinear stochastic fractional systems with distributed delays in control, Journal of control and decision. 1-16, (2017) https://doi.org/10.1080/23307706.2017.1297690
- 16.Muthukumar, P., Thiagu, K.: 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. Journal of Dynamical and Control Systems 23, 213–235 (2017)MathSciNetCrossRefGoogle Scholar
- 21.Rajivganthi, C., Muthukumar, P., Ganesh Priya, B.: Approximate controllability of fractional stochastic integrodifferential equations with infinite delay of order \(1<\alpha <2\), IMA Journal of Mathematical Control and Information. 1–15, (2015)Google Scholar
- 27.Santos, J.P.C., Cuevas, C., Andrade, B.: Existence results for a fractional equations with state dependent delay, Advances in Difference Equations, 2011 (2011), Article ID 642013Google Scholar
- 29.Andrade, B.D., Santos, J.P.C.: Existence of solutions for a fractional neutral integro differential equation with unbounded delay. Electron. J 2012, 1–13 (2012)Google Scholar