IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v166y2023ics0960077922010852.html
   My bibliography  Save this article

Darboux problem for proportional partial fractional differential equations

Author

Listed:
  • Ben Makhlouf, Abdellatif
  • Benjemaa, Mondher
  • Boucenna, Djalal
  • Hammami, Mohamed Ali

Abstract

In this paper, we introduce and study a novel fractional derivative called the generalized proportional Caputo fractional derivative. Under adequate assumptions on the source term, we prove existence and uniqueness aspects of the Darboux problems involving the generalized proportional fractional operator. A numerical scheme based on finite differences approximation is also investigated, and results of convergence are established. Several numerical tests are performed in illustration.

Suggested Citation

  • Ben Makhlouf, Abdellatif & Benjemaa, Mondher & Boucenna, Djalal & Hammami, Mohamed Ali, 2023. "Darboux problem for proportional partial fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010852
    DOI: 10.1016/j.chaos.2022.112906
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922010852
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112906?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. Ravi Agarwal & Snezhana Hristova, 2022. "Impulsive Memristive Cohen–Grossberg Neural Networks Modeled by Short Term Generalized Proportional Caputo Fractional Derivative and Synchronization Analysis," Mathematics, MDPI, vol. 10(13), pages 1-12, July.
    2. Balamurali Ramakrishnan & Murat Erhan Cimen & Akif Akgul & Chunbiao Li & Karthikeyan Rajagopal & Hakan Kor & Abdellatif Ben Makhlouf, 2022. "Chaotic Oscillations in a Fractional-Order Circuit with a Josephson Junction Resonator and Its Synchronization Using Fuzzy Sliding Mode Control," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-11, August.
    3. Abdellatif Boutiara & Mohammed K. A. Kaabar & Zailan Siri & Mohammad Esmael Samei & Xiao-Guang Yue & Abdellatif Ben Makhlouf, 2022. "Investigation of the Generalized Proportional Langevin and Sturm–Liouville Fractional Differential Equations via Variable Coefficients and Antiperiodic Boundary Conditions with a Control Theory Appl," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-21, April.
    4. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
    5. He, Lin & Wang, Yangyang & Wei, Yujiang & Wang, Mingwei & Hu, Xiaosong & Shi, Qin, 2022. "An adaptive central difference Kalman filter approach for state of charge estimation by fractional order model of lithium-ion battery," Energy, Elsevier, vol. 244(PA).
    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. Edgardo Alvarez & Carlos Lizama, 2020. "The Super-Diffusive Singular Perturbation Problem," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    2. Angstmann, C.N. & Henry, B.I. & Jacobs, B.A. & McGann, A.V., 2017. "A time-fractional generalised advection equation from a stochastic process," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 175-183.
    3. Soma Dhar & Lipi B. Mahanta & Kishore Kumar Das, 2019. "Formulation Of The Simple Markovian Model Using Fractional Calculus Approach And Its Application To Analysis Of Queue Behaviour Of Severe Patients," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 117-129, March.
    4. Saif Eddin Jabari & Nikolaos M. Freris & Deepthi Mary Dilip, 2020. "Sparse Travel Time Estimation from Streaming Data," Transportation Science, INFORMS, vol. 54(1), pages 1-20, January.
    5. Katarzyna Górska & Andrzej Horzela, 2021. "Non-Debye Relaxations: Two Types of Memories and Their Stieltjes Character," Mathematics, MDPI, vol. 9(5), pages 1-13, February.
    6. Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
    7. Goswami, Koushik, 2021. "Work fluctuations in a generalized Gaussian active bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    8. Virginia Kiryakova, 2021. "A Guide to Special Functions in Fractional Calculus," Mathematics, MDPI, vol. 9(1), pages 1-40, January.
    9. Yang, Bowen & Wang, Dafang & Sun, Xu & Chen, Shiqin & Wang, Xingcheng, 2023. "Offline order recognition for state estimation of Lithium-ion battery using fractional order model," Applied Energy, Elsevier, vol. 341(C).
    10. Murat A. Sultanov & Durdimurod K. Durdiev & Askar A. Rahmonov, 2021. "Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential Equation," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    11. Zhu, Yunlong & Dong, Zhe & Cheng, Zhonghua & Huang, Xiaojin & Dong, Yujie & Zhang, Zuoyi, 2023. "Neural network extended state-observer for energy system monitoring," Energy, Elsevier, vol. 263(PA).
    12. Vieira, N. & Ferreira, M. & Rodrigues, M.M., 2022. "Time-fractional telegraph equation with ψ-Hilfer derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    13. Iomin, A. & Zaburdaev, V. & Pfohl, T., 2016. "Reaction front propagation of actin polymerization in a comb-reaction system," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 115-122.
    14. Sánchez, Ewin, 2019. "Burr type-XII as a superstatistical stationary distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 443-446.
    15. Serkan Araci & Gauhar Rahman & Abdul Ghaffar & Azeema & Kottakkaran Sooppy Nisar, 2019. "Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    16. Charles K. Amponsah & Tomasz J. Kozubowski & Anna K. Panorska, 2021. "A general stochastic model for bivariate episodes driven by a gamma sequence," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-31, December.
    17. Iomin, A., 2016. "Quantum continuous time random walk in nonlinear Schrödinger equation with disorder," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 64-70.
    18. Qian, Wei & Li, Wan & Guo, Xiangwei & Wang, Haoyu, 2024. "A switching gain adaptive sliding mode observer for SoC estimation of lithium-ion battery," Energy, Elsevier, vol. 292(C).
    19. Najma Ahmed & Nehad Ali Shah & Farman Ali & Dumitru Vieru & F.D. Zaman, 2021. "Analytical Solutions of the Fractional Mathematical Model for the Concentration of Tumor Cells for Constant Killing Rate," Mathematics, MDPI, vol. 9(10), pages 1-14, May.
    20. Hainaut, Donatien, 2021. "Lévy interest rate models with a long memory," LIDAM Discussion Papers ISBA 2021020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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:166:y:2023:i:c:s0960077922010852. 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.