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Controllability for a class of fractional neutral integro-differential equations with unbounded delay

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  • Vijayakumar, V.
  • Selvakumar, A.
  • Murugesu, R.

Abstract

In this paper, we consider a class of fractional neutral integro-differential equations with unbounded delay in Banach spaces. This paper deals with the exact controllability for fractional integro-differential neutral control systems. First, we establish a new set of sufficient conditions for the exact controllability of nonlinear fractional systems by using a fixed point analysis approach. Further, we extend the result to study the exact controllability concept with nonlocal conditions. Examples are provided to illustrate our main results.

Suggested Citation

  • Vijayakumar, V. & Selvakumar, A. & Murugesu, R., 2014. "Controllability for a class of fractional neutral integro-differential equations with unbounded delay," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 303-312.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:303-312
    DOI: 10.1016/j.amc.2014.01.029
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    References listed on IDEAS

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    1. M. Benchohra & E.P. Gatsori & S.K. Ntouyas, 2003. "Controllability Results for Semilinear Evolution Inclusions with Nonlocal Conditions," Journal of Optimization Theory and Applications, Springer, vol. 118(3), pages 493-513, September.
    2. Chang, Yong-Kui & Anguraj, A. & Mallika Arjunan, M., 2009. "Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1864-1876.
    3. B. Liu, 2004. "Controllability of Neutral Functional Differential and Integrodifferential Inclusions with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 573-593, December.
    4. Ludwik Byszewski & Haydar Akca, 1997. "On a mild solution of a semilinear functional-differential evolution nonlocal problem," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-7, January.
    5. M. Benchohra & S.K. Ntouyas, 2002. "Controllability for Functional Differential and Integrodifferential Inclusions in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 449-472, June.
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    Cited by:

    1. Hamdy M. Ahmed & Mahmoud M. El-Borai & Hassan M. El-Owaidy & Ahmed S. Ghanem, 2019. "Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    2. Wang, Qi, 2015. "Numerical oscillation of neutral logistic delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 49-59.
    3. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.

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