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Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

Author

Listed:
  • Mourad Kerboua
  • Amar Debbouche
  • Dumitru Baleanu

Abstract

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

Suggested Citation

  • Mourad Kerboua & Amar Debbouche & Dumitru Baleanu, 2013. "Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:262191
    DOI: 10.1155/2013/262191
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    References listed on IDEAS

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    1. Nemat Nyamoradi & Dumitru Baleanu & Tahereh Bashiri, 2013. "Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-20, June.
    2. Nemat Nyamoradi & Dumitru Baleanu & Tahereh Bashiri, 2013. "Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Bashir Ahmad & Sotiris K. Ntouyas, 2012. "A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, April.
    4. Amar Debbouche & Dumitru Baleanu, 2012. "Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Bashir Ahmad & Sotiris K. Ntouyas, 2012. "A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Amar Debbouche & Dumitru Baleanu, 2012. "Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, September.
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