IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v339y2018icp516-534.html
   My bibliography  Save this article

Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions

Author

Listed:
  • Ahmad, Bashir
  • Luca, Rodica

Abstract

We investigate the existence of solutions for Caputo type sequential fractional integro-differential equations and inclusions subject to nonlocal boundary conditions involving Riemann–Liouville and Riemann–Stieltjes integrals. For the proofs of our main theorems we use the contraction mapping principle and the Krasnosel’skii fixed point theorem for the sum of two operators in the case of fractional equations, and the nonlinear alternative of Leray–Schauder type for Kakutani maps and the Covitz–Nadler fixed point theorem in the case of fractional inclusions. Some examples are presented to illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:516-534
    DOI: 10.1016/j.amc.2018.07.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318305836
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.07.025?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. 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.
    2. 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.
    3. 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.
    4. Jia, Mei & Liu, Xiping, 2014. "Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 313-323.
    5. J. Caballero & I. Cabrera & K. Sadarangani, 2012. "Positive Solutions of Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, October.
    6. 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.
    7. 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.
    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. Johnny Henderson & Rodica Luca & Alexandru Tudorache, 2021. "Positive Solutions for a System of Coupled Semipositone Fractional Boundary Value Problems with Sequential Fractional Derivatives," Mathematics, MDPI, vol. 9(7), pages 1-22, April.
    2. Ahmed Alsaedi & Rodica Luca & Bashir Ahmad, 2020. "Existence of Positive Solutions for a System of Singular Fractional Boundary Value Problems with p -Laplacian Operators," Mathematics, MDPI, vol. 8(11), pages 1-18, October.
    3. Wei Zhang & Wenbin Liu, 2020. "Existence of Solutions for Fractional Multi-Point Boundary Value Problems on an Infinite Interval at Resonance," Mathematics, MDPI, vol. 8(1), pages 1-22, January.
    4. Shahram Rezapour & Sotiris K. Ntouyas & Abdelkader Amara & Sina Etemad & Jessada Tariboon, 2021. "Some Existence and Dependence Criteria of Solutions to a Fractional Integro-Differential Boundary Value Problem via the Generalized Gronwall Inequality," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    5. Bashir Ahmad & Abrar Broom & Ahmed Alsaedi & Sotiris K. Ntouyas, 2020. "Nonlinear Integro-Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals with Nonlocal Boundary Data," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    6. Ahmed Alsaedi & Amjad F. Albideewi & Sotiris K. Ntouyas & Bashir Ahmad, 2020. "On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions," Mathematics, MDPI, vol. 8(11), pages 1-14, October.
    7. Fang Wang & Lishan Liu & Yonghong Wu & Yumei Zou, 2019. "Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p -Laplacian Operator," Complexity, Hindawi, vol. 2019, pages 1-21, October.
    8. Ahmed Salem & Faris Alzahrani & Lamya Almaghamsi, 2019. "Fractional Langevin Equations with Nonlocal Integral Boundary Conditions," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    9. 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.

    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. 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. 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. 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).
    4. 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.
    5. 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.
    6. Liu, Xiping & Jia, Mei, 2019. "Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 230-242.
    7. 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.
    8. Ahmed Alsaedi & Rodica Luca & Bashir Ahmad, 2020. "Existence of Positive Solutions for a System of Singular Fractional Boundary Value Problems with p -Laplacian Operators," Mathematics, MDPI, vol. 8(11), pages 1-18, October.
    9. Ahmed Salem & Faris Alzahrani & Lamya Almaghamsi, 2019. "Fractional Langevin Equations with Nonlocal Integral Boundary Conditions," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    10. Johnny Henderson & Rodica Luca & Alexandru Tudorache, 2021. "Positive Solutions for a System of Coupled Semipositone Fractional Boundary Value Problems with Sequential Fractional Derivatives," Mathematics, MDPI, vol. 9(7), pages 1-22, April.
    11. 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).
    12. Nemat Nyamoradi & Sotiris K. Ntouyas & Jessada Tariboon, 2022. "Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations Involving the Hadamard Derivatives," Mathematics, MDPI, vol. 10(17), pages 1-15, August.
    13. Muthaiah Subramanian & Jehad Alzabut & Mohamed I. Abbas & Chatthai Thaiprayoon & Weerawat Sudsutad, 2022. "Existence of Solutions for Coupled Higher-Order Fractional Integro-Differential Equations with Nonlocal Integral and Multi-Point Boundary Conditions Depending on Lower-Order Fractional Derivatives and," Mathematics, MDPI, vol. 10(11), pages 1-19, May.
    14. Shahram Rezapour & Salim Ben Chikh & Abdelkader Amara & Sotiris K. Ntouyas & Jessada Tariboon & Sina Etemad, 2021. "Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems," Mathematics, MDPI, vol. 9(7), pages 1-17, March.
    15. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    16. 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.
    17. 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.
    18. 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.
    19. Bashir Ahmad & Ahmed Alsaedi & Sotiris K. Ntouyas & Hamed H. Al-Sulami, 2019. "On Neutral Functional Differential Inclusions involving Hadamard Fractional Derivatives," Mathematics, MDPI, vol. 7(11), pages 1-13, November.
    20. 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.

    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:apmaco:v:339:y:2018:i:c:p:516-534. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.