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Control Systems Described by a Class of Fractional Semilinear Evolution Equations and Their Relaxation Property

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  • Xiaoyou Liu
  • Xi Fu

Abstract

We consider a control system described by a class of fractional semilinear evolution equations in a separable reflexive Banach space. The constraint on the control is a multivalued map with nonconvex values which is lower semicontinuous with respect to the state variable. Along with the original system we also consider the system in which the constraint on the control is the upper semicontinuous convex‐valued regularization of the original constraint. We obtain the existence results for the control systems and the relaxation property between the solution sets of these systems.

Suggested Citation

  • Xiaoyou Liu & Xi Fu, 2012. "Control Systems Described by a Class of Fractional Semilinear Evolution Equations and Their Relaxation Property," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:850529
    DOI: 10.1155/2012/850529
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Bashir Ahmad & Ahmed Alsaedi & Naseer Shahzad, 2012. "On the Dimension of the Solution Set for Semilinear Fractional Differential Inclusions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. 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.
    3. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
    4. 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).
    5. Ravi P. Agarwal & Bashir Ahmad & Ahmed Alsaedi & Naseer Shahzad, 2012. "On the Dimension of the Solution Set for Semilinear Fractional Differential Inclusions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, May.
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