IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v83y2016icp234-241.html
   My bibliography  Save this article

On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions

Author

Listed:
  • Ahmad, Bashir
  • Ntouyas, Sotiris K.
  • Alsaedi, Ahmed

Abstract

We investigate a coupled system of fractional differential equations with nonlinearities depending on the unknown functions as well as their lower order fractional derivatives supplemented with coupled nonlocal and integral boundary conditions. We emphasize that the problem considered in the present setting is new and provides further insight into the study of nonlocal nonlinear coupled boundary value problems. We present two results in this paper: the first one dealing with the uniqueness of solutions for the given problem is established by applying contraction mapping principle, while the second one concerning the existence of solutions is obtained via Leray–Schauder’s alternative. The main results are well illustrated with the aid of examples.

Suggested Citation

  • Ahmad, Bashir & Ntouyas, Sotiris K. & Alsaedi, Ahmed, 2016. "On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 234-241.
    • Handle: RePEc:eee:chsofr:v:83:y:2016:i:c:p:234-241
    DOI: 10.1016/j.chaos.2015.12.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077915004324
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.12.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ge, Zheng-Ming & Ou, Chan-Yi, 2008. "Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 705-717.
    2. Ahmad, Bashir & K. Ntouyas, Sotiris, 2015. "Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 615-622.
    3. Bashir Ahmad & Sotiris K. Ntouyas & Ahmed Alsaedi, 2013. "A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, March.
    4. Duan, Jun-Sheng & Wang, Zhong & Liu, Yu-Lu & Qiu, Xiang, 2013. "Eigenvalue problems for fractional ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 46-53.
    5. Ge, Zheng-Ming & Jhuang, Wei-Ren, 2007. "Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 270-289.
    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. Ahmad, Bashir & Luca, Rodica, 2017. "Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 378-388.
    2. Ding, Dawei & Yan, Jie & Wang, Nian & Liang, Dong, 2017. "Pinning synchronization of fractional order complex-variable dynamical networks with time-varying coupling," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 41-50.
    3. Aljoudi, Shorog & Ahmad, Bashir & Nieto, Juan J. & Alsaedi, Ahmed, 2016. "A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 39-46.
    4. Ahmad, Bashir & Luca, Rodica, 2018. "Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 516-534.
    5. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    6. Almalahi, Mohammed A. & Panchal, Satish K. & Jarad, Fahd, 2021. "Stability results of positive solutions for a system of ψ -Hilfer fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

    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. Nazim I Mahmudov & Sameer Bawaneh & Areen Al-Khateeb, 2019. "On a Coupled System of Fractional Differential Equations with Four Point Integral Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    2. Agarwal, Ravi P. & Ahmad, Bashir & Garout, Doa’a & Alsaedi, Ahmed, 2017. "Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 149-161.
    3. Ahmad, Bashir & Luca, Rodica, 2018. "Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 516-534.
    4. Longfei Lin & Yansheng Liu & Daliang Zhao, 2021. "Study on Implicit-Type Fractional Coupled System with Integral Boundary Conditions," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    5. Deng, Hongmin & Li, Tao & Wang, Qionghua & Li, Hongbin, 2009. "A fractional-order hyperchaotic system and its synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 962-969.
    6. Abdelkader Moumen & Abdelaziz Mennouni & Mohamed Bouye, 2023. "A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    7. Nazim I Mahmudov & Areen Al-Khateeb, 2019. "Stability, Existence and Uniqueness of Boundary Value Problems for a Coupled System of Fractional Differential Equations," Mathematics, MDPI, vol. 7(4), pages 1-12, April.
    8. Aljoudi, Shorog & Ahmad, Bashir & Nieto, Juan J. & Alsaedi, Ahmed, 2016. "A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 39-46.
    9. Hallaji, Majid & Dideban, Abbas & Khanesar, Mojtaba Ahmadieh & kamyad, Ali vahidyan, 2018. "Optimal synchronization of non-smooth fractional order chaotic systems with uncertainty based on extension of a numerical approach in fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 325-340.
    10. Al-Mdallal, Qasem M., 2018. "On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 261-267.
    11. He, Ying & Zuo, Qian, 2021. "Jacobi-Davidson method for the second order fractional eigenvalue problems," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    12. Bashir Ahmad & Ymnah Alruwaily & Ahmed Alsaedi & Sotiris K. Ntouyas, 2019. "Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    13. Chunlai Li & Jing Zhang, 2016. "Synchronisation of a fractional-order chaotic system using finite-time input-to-state stability," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2440-2448, July.
    14. Longfei Lin & Yansheng Liu & Daliang Zhao, 2021. "Controllability of Impulsive ψ -Caputo Fractional Evolution Equations with Nonlocal Conditions," Mathematics, MDPI, vol. 9(12), pages 1-14, June.
    15. Yu, Yongguang & Li, Han-Xiong, 2008. "The synchronization of fractional-order Rössler hyperchaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1393-1403.
    16. Sina Etemad & Sotiris K. Ntouyas & Bashir Ahmad & Shahram Rezapour & Jessada Tariboon, 2022. "Sequential Fractional Hybrid Inclusions: A Theoretical Study via Dhage’s Technique and Special Contractions," Mathematics, MDPI, vol. 10(12), pages 1-27, June.
    17. Jarunee Soontharanon & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2019. "A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line," Mathematics, MDPI, vol. 7(3), pages 1-22, March.
    18. Ahmad, Bashir & Luca, Rodica, 2017. "Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 378-388.
    19. Li, Jing & Qi, Jiangang, 2015. "Eigenvalue problems for fractional differential equations with right and left fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 1-10.
    20. Fathy, Mohamed & Abdelgaber, K.M., 2022. "Approximate solutions for the fractional order quadratic Riccati and Bagley-Torvik differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

    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:eee:chsofr:v:83:y:2016:i:c:p:234-241. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.