IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i1p79-d197482.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/1/79/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/1/79/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Shruti Agarwal & Dhirendra Bahuguna, 2006. "Existence of solutions to Sobolev-type partial neutral differential equations," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-10, March.
    4. Tamilalagan, P. & Balasubramaniam, P., 2017. "Moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 299-307.
    5. Du, Wenbo & Zhang, Mingyuan & Ying, Wen & Perc, Matjaž & Tang, Ke & Cao, Xianbin & Wu, Dapeng, 2018. "The networked evolutionary algorithm: A network science perspective," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 33-43.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    2. Ahmed, Hamdy M. & Zhu, Quanxin, 2023. "Exploration nonlocal controllability for Hilfer fractional differential inclusions with Clarke subdifferential and nonlinear noise," Statistics & Probability Letters, Elsevier, vol. 195(C).
    3. Qian, Qian & Chao, Xiangrui & Feng, Hairong, 2023. "Internal or external control? How to respond to credit risk contagion in complex enterprises network," International Review of Financial Analysis, Elsevier, vol. 87(C).
    4. Wang, Jianwei & Xu, Wenshu & Chen, Wei & Yu, Fengyuan & He, Jialu, 2021. "Information sharing can suppress the spread of epidemics: Voluntary vaccination game on two-layer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    5. Elimhan N. Mahmudov, 2018. "Optimization of Mayer Problem with Sturm–Liouville-Type Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 345-375, May.
    6. Wang, Qi, 2015. "Numerical oscillation of neutral logistic delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 49-59.
    7. Eduardo Hernández & Donal O’Regan & Krishnan Balachandran, 2013. "Comments on Some Recent Results on Controllability of Abstract Differential Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 292-295, October.
    8. Elimhan N. Mahmudov, 2022. "Optimization of Higher-Order Differential Inclusions with Special Boundary Value Conditions," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 36-55, January.
    9. Yan, Zheping & Zhang, Jinzhong & Zeng, Jia & Tang, Jialing, 2021. "Nature-inspired approach: An enhanced whale optimization algorithm for global optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 17-46.
    10. Li, Xiaosi & Li, Jiayi & Yang, Haichuan & Wang, Yirui & Gao, Shangce, 2022. "Population interaction network in representative differential evolution algorithms: Power-law outperforms Poisson distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    11. Zhao, Li & Li, Yuqi & Li, Shuai & Ke, Hanchen, 2023. "A frequency item mining based embedded feature selection algorithm and its application in energy consumption prediction of electric bus," Energy, Elsevier, vol. 271(C).
    12. Yang, Han-Xin & Sun, Lei, 2020. "Heterogeneous donation game in geographical small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    13. Wang, Chunyu & Zhang, Fan & Deng, Yue & Gao, Chao & Li, Xianghua & Wang, Zhen, 2020. "An adaptive population control framework for ACO-based community detection," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    14. Dhayal, Rajesh & Malik, Muslim, 2021. "Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    15. Chao, Xiangrui & Ran, Qin & Chen, Jia & Li, Tie & Qian, Qian & Ergu, Daji, 2022. "Regulatory technology (Reg-Tech) in financial stability supervision: Taxonomy, key methods, applications and future directions," International Review of Financial Analysis, Elsevier, vol. 80(C).
    16. Kutlu Onay, Funda & Aydemı̇r, Salih Berkan, 2022. "Chaotic hunger games search optimization algorithm for global optimization and engineering problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 514-536.
    17. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
    18. Irshad Ahmad & Saeed Ahmad & Ghaus ur Rahman & Shabir Ahmad & Manuel De la Sen, 2022. "Controllability and Observability Results of an Implicit Type Fractional Order Delay Dynamical System," Mathematics, MDPI, vol. 10(23), pages 1-24, November.
    19. Liang, Jin & Yang, He, 2015. "Controllability of fractional integro-differential evolution equations with nonlocal conditions," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 20-29.
    20. Wang, Lei & Li, Shouwei & Chen, Tingqiang, 2019. "Investor behavior, information disclosure strategy and counterparty credit risk contagion," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 37-49.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:79-:d:197482. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.