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Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System

Author

Listed:
  • Hamdy M. Ahmed

    (Higher Institute of Engineering, El-Shorouk Academy, P.O. Box 3, El-Shorouk City, Cairo, Egypt)

  • Mahmoud M. El-Borai

    (Department of Mathematics, Faculty of Science, Alexandria University, P.O. Box 21515, Alexandria, Egypt)

  • Hassan M. El-Owaidy

    (Department of Mathematics, Faculty of Science, Al-Azhar University, P.O. Box 11511, Cairo, Egypt)

  • Ahmed S. Ghanem

    (Higher Institute of Engineering, El-Shorouk Academy, P.O. Box 3, El-Shorouk City, Cairo, Egypt)

Abstract

Fractional integro-differential equations arise in the mathematical modeling of various physical phenomena like heat conduction in materials with memory, diffusion processes, etc. In this manuscript, we prove the existence of mild solution for Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2 . We establish the sufficient conditions for the approximate controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2 . In addition, we prove the exact null controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2 . Finally, an example is given to illustrate the obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:79-:d:197482
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    References listed on IDEAS

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    2. Yan, Zuomao & Lu, Fangxia, 2017. "Approximate controllability of a multi-valued fractional impulsive stochastic partial integro-differential equation with infinite delay," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 425-447.
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    4. Zhenhai Liu & Maojun Bin, 2013. "Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-17, December.
    5. 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.
    6. G. Arthi & K. Balachandran, 2012. "Controllability of Damped Second-Order Impulsive Neutral Functional Differential Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 799-813, March.
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    Cited by:

    1. Yazid Alhojilan & Hamdy M. Ahmed, 2023. "New Results Concerning Approximate Controllability of Conformable Fractional Noninstantaneous Impulsive Stochastic Evolution Equations via Poisson Jumps," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    2. Asmae Tajani & Fatima-Zahrae El Alaoui, 2023. "Boundary Controllability of Riemann–Liouville Fractional Semilinear Evolution Systems," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 767-780, August.

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