IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i4p341-d221227.html

Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations

Author

Listed:
  • Zeeshan Ali

    (Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan)

  • Poom Kumam

    (Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Kamal Shah

    (Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18800, Pakistan)

  • Akbar Zada

    (Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan)

Abstract

This manuscript deals with the existence theory, uniqueness, and various kinds of Ulam–Hyers stability of solutions for a class and coupled system of fractional order differential equations involving Caputo derivatives. Applying Schaefer and Banach’s fixed point approaches, existence and uniqueness results are obtained for the proposed problems. Stability results are investigated by using the classical technique of nonlinear functional analysis. Examples are given with each problem to illustrate the main results.

Suggested Citation

  • Zeeshan Ali & Poom Kumam & Kamal Shah & Akbar Zada, 2019. "Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations," Mathematics, MDPI, vol. 7(4), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:341-:d:221227
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/4/341/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/4/341/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gafiychuk, V. & Datsko, B. & Meleshko, V. & Blackmore, D., 2009. "Analysis of the solutions of coupled nonlinear fractional reaction–diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1095-1104.
    2. Naveed Ahmad & Zeeshan Ali & Kamal Shah & Akbar Zada & Ghaus ur Rahman, 2018. "Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations," Complexity, Hindawi, vol. 2018, pages 1-15, February.
    3. Nigmatullin, Raul R. & Omay, Tolga & Baleanu, Dumitru, 2010. "On fractional filtering versus conventional filtering in economics," MPRA Paper 111643, University Library of Munich, Germany.
    4. Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-9, July.
    5. Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher‐Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    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. Akbar Zada & Shaheen Fatima & Zeeshan Ali & Jiafa Xu & Yujun Cui, 2019. "Stability Results for a Coupled System of Impulsive Fractional Differential Equations," Mathematics, MDPI, vol. 7(10), pages 1-29, October.
    2. Wuyang Wang & Khansa Hina Khalid & Akbar Zada & Sana Ben Moussa & Jun Ye, 2023. "q -Fractional Langevin Differential Equation with q -Fractional Integral Conditions," Mathematics, MDPI, vol. 11(9), pages 1-27, May.
    3. Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.

    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. Sotiris K. Ntouyas & Phollakrit Wongsantisuk & Ayub Samadi & Jessada Tariboon, 2024. "Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function," Mathematics, MDPI, vol. 12(7), pages 1-21, April.
    2. Min Jiang & Shouming Zhong, 2014. "Existence and Multiple Positive Solutions for Boundary Value Problem of Fractional Differential Equation with p‐Laplacian Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Rafia Majeed & Binlin Zhang & Mehboob Alam, 2023. "Fractional Langevin Coupled System with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    4. Jiqiang Jiang & Lishan Liu & Yonghong Wu, 2012. "Positive Solutions for Nonlinear Fractional Differential Equations with Boundary Conditions Involving Riemann‐Stieltjes Integrals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Yansheng Liu, 2013. "Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Azarnavid, Babak & Emamjomeh, Mahdi & Nabati, Mohammad, 2022. "A shooting like method based on the shifted Chebyshev polynomials for solving nonlinear fractional multi-point boundary value problem," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    7. Wenning Liu & Xingjie Yan & Wei Qi, 2014. "Positive Solutions for Coupled Nonlinear Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    8. Wen-Xue Zhou & Hai-Zhong Liu, 2012. "Existence of Weak Solutions for Nonlinear Fractional Differential Inclusion with Nonseparated Boundary Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    9. N. I. Mahmudov & S. Unul, 2014. "Existence of Solutions of α ∈ (2,3] Order Fractional Three‐Point Boundary Value Problems with Integral Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    10. Lihong Zhang & Bashir Ahmad & Guotao Wang & Ravi P. Agarwal & Maryem Al-Yami & Wafa Shammakh, 2013. "Nonlocal Integrodifferential Boundary Value Problem for Nonlinear Fractional Differential Equations on an Unbounded Domain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Mujeeb Ur Rehman & Rahmat Ali Khan, 2010. "Positive Solutions to Nonlinear Higher‐Order Nonlocal Boundary Value Problems for Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    12. Guotao Wang & Bashir Ahmad & Lihong Zhang, 2012. "On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    13. Yulin Zhao & Li Huang & Xuebin Wang & Xianyang Zhu, 2012. "Existence of Solutions for Fractional Integro‐Differential Equation with Multipoint Boundary Value Problem in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    14. Liping Wang & Zongfu Zhou & Hui Zhou, 2014. "Positive Solutions for Singular p‐Laplacian Fractional Differential System with Integral Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    15. Guotao Wang & Bashir Ahmad & Lihong Zhang, 2012. "A Coupled System of Nonlinear Fractional Differential Equations with Multipoint Fractional Boundary Conditions on an Unbounded Domain," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    16. Meysam Alvan & Rahmat Darzi & Amin Mahmoodi, 2016. "Existence Results for a New Class of Boundary Value Problems of Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 4(1), pages 1-10, March.
    17. Jing Zhao & Peifen Lu & Yiliang Liu, 2013. "Existence and Numerical Simulation of Solutions for Fractional Equations Involving Two Fractional Orders with Nonlocal Boundary Conditions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    18. Hasanov, Mübariz & Araç, Aysen & Telatar, Funda, 2010. "Nonlinearity and structural stability in the Phillips curve: Evidence from Turkey," Economic Modelling, Elsevier, vol. 27(5), pages 1103-1115, September.
    19. Caicedo, Alejandro & Cuevas, Claudio & Mateus, Éder & Viana, Arlúcio, 2021. "Global solutions for a strongly coupled fractional reaction-diffusion system in Marcinkiewicz spaces," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    20. Akbar Zada & Shaheen Fatima & Zeeshan Ali & Jiafa Xu & Yujun Cui, 2019. "Stability Results for a Coupled System of Impulsive Fractional Differential Equations," Mathematics, MDPI, vol. 7(10), pages 1-29, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:4:p:341-:d:221227. 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 The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (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.