IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2020y2020i1n8898292.html

Existence Results for a Class of Coupled Hilfer Fractional Pantograph Differential Equations with Nonlocal Integral Boundary Value Conditions

Author

Listed:
  • Karim Guida
  • Khalid Hilal
  • Lahcen Ibnelazyz

Abstract

This paper deals with the existence and uniqueness of solutions for a new class of coupled systems of Hilfer fractional pantograph differential equations with nonlocal integral boundary conditions. First of all, we are going to give some definitions that are necessary for the understanding of the manuscript; second of all, we are going to prove our main results using the fixed point theorems, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem; in the end, we are giving two examples to illustrate our results.

Suggested Citation

  • Karim Guida & Khalid Hilal & Lahcen Ibnelazyz, 2020. "Existence Results for a Class of Coupled Hilfer Fractional Pantograph Differential Equations with Nonlocal Integral Boundary Value Conditions," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:8898292
    DOI: 10.1155/2020/8898292
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2020/8898292
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2020/8898292?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
    ---><---

    References listed on IDEAS

    as
    1. Yassine Benia & Marianna Ruggieri & Andrea Scapellato, 2019. "Exact Solutions for a Modified Schrödinger Equation," Mathematics, MDPI, vol. 7(10), pages 1-9, September.
    2. Wang, JinRong & Zhang, Yuruo, 2015. "Nonlocal initial value problems for differential equations with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 850-859.
    3. Gu, Haibo & Trujillo, Juan J., 2015. "Existence of mild solution for evolution equation with Hilfer fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 344-354.
    4. Bahşı, M. Mustafa & Çevik, Mehmet & Sezer, Mehmet, 2015. "Orthoexponential polynomial solutions of delay pantograph differential equations with residual error estimation," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 11-21.
    Full references (including those not matched with items on IDEAS)

    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. Athasit Wongcharoen & Bashir Ahmad & Sotiris K. Ntouyas & Jessada Tariboon, 2020. "Three‐Point Boundary Value Problems for the Langevin Equation with the Hilfer Fractional Derivative," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    2. Surang Sitho & Sotiris K. Ntouyas & Ayub Samadi & Jessada Tariboon, 2021. "Boundary Value Problems for ψ -Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions," Mathematics, MDPI, vol. 9(9), pages 1-18, April.
    3. 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.
    4. Gou, Haide & Li, Baolin, 2018. "Study on the mild solution of Sobolev type Hilfer fractional evolution equations with boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 168-179.
    5. Athasit Wongcharoen & Sotiris K. Ntouyas & Phollakrit Wongsantisuk & Jessada Tariboon, 2021. "Existence Results for a Nonlocal Coupled System of Sequential Fractional Differential Equations Involving ψ‐Hilfer Fractional Derivatives," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    6. Nawapol Phuangthong & Sotiris K. Ntouyas & Jessada Tariboon & Kamsing Nonlaopon, 2021. "Nonlocal Sequential Boundary Value Problems for Hilfer Type Fractional Integro-Differential Equations and Inclusions," Mathematics, MDPI, vol. 9(6), pages 1-19, March.
    7. Ahmed, Hamdy M. & El-Borai, Mahmoud M., 2018. "Hilfer fractional stochastic integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 182-189.
    8. Athasit Wongcharoen & Sotiris K. Ntouyas & Jessada Tariboon, 2020. "Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions," Mathematics, MDPI, vol. 8(11), pages 1-11, October.
    9. Nisar, Kottakkaran Sooppy & Jothimani, K. & Kaliraj, K. & Ravichandran, C., 2021. "An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Guotao Wang & Jianfang Qin & Huanhe Dong & Tingting Guan, 2019. "Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System," Mathematics, MDPI, vol. 7(6), pages 1-10, June.
    11. Kavitha, K. & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on controllability of Hilfer fractional neutral differential equations with infinite delay via measures of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    12. Karim Guida & Khalid Hilal & Lahcen Ibnelazyz, 2020. "Existence of Mild Solutions for a Class of Impulsive Hilfer Fractional Coupled Systems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    13. Dhayal, Rajesh & Zhu, Quanxin, 2023. "Stability and controllability results of ψ-Hilfer fractional integro-differential systems under the influence of impulses," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    14. Boudjerida, Assia & Seba, Djamila, 2021. "Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    15. Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2018. "Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 433-453.
    16. Sivajiganesan Sivasankar & Ramalingam Udhayakumar & Velmurugan Subramanian & Ghada AlNemer & Ahmed M. Elshenhab, 2022. "Existence of Hilfer Fractional Stochastic Differential Equations with Nonlocal Conditions and Delay via Almost Sectorial Operators," Mathematics, MDPI, vol. 10(22), pages 1-18, November.
    17. Sousa, J. Vanterler da C. & Oliveira, D.S. & Capelas de Oliveira, E., 2021. "A note on the mild solutions of Hilfer impulsive fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    18. Abbas, Saïd & Benchohra, Mouffak & Lazreg, Jamal-Eddine & Zhou, Yong, 2017. "A survey on Hadamard and Hilfer fractional differential equations: Analysis and stability," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 47-71.
    19. Yong Zhou, 2022. "Infinite Interval Problems for Fractional Evolution Equations," Mathematics, MDPI, vol. 10(6), pages 1-13, March.
    20. Anbu Dhanush & Velusamy Vijayakumar, 2026. "Time-Optimal Control of Hilfer Fractional Stochastic Hemivariational Inequalities Analysis," Journal of Optimization Theory and Applications, Springer, vol. 208(3), pages 1-31, March.

    More about this item

    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:wly:jnlamp:v:2020:y:2020:i:1:n:8898292. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3197 .

    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.