IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v212y2023icp224-233.html
   My bibliography  Save this article

A new fractional derivative operator with generalized cardinal sine kernel: Numerical simulation

Author

Listed:
  • Odibat, Zaid
  • Baleanu, Dumitru

Abstract

In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann–Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus.

Suggested Citation

  • Odibat, Zaid & Baleanu, Dumitru, 2023. "A new fractional derivative operator with generalized cardinal sine kernel: Numerical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 224-233.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:224-233
    DOI: 10.1016/j.matcom.2023.04.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423002033
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.04.033?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. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
    2. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.
    3. Mohammed Al-Refai & Dumitru Baleanu, 2022. "On An Extension Of The Operator With Mittag-Leffler Kernel," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-7, August.
    4. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    5. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    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. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    3. Fouladi, Somayeh & Dahaghin, Mohammad Shafi, 2022. "Numerical investigation of the variable-order fractional Sobolev equation with non-singular Mittag–Leffler kernel by finite difference and local discontinuous Galerkin methods," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Nazir, Aqsa & Ahmed, Naveed & Khan, Umar & Mohyud-din, Syed Tauseef, 2020. "On stability of improved conformable model for studying the dynamics of a malnutrition community," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    5. Abdalla, Bahaaeldin & Abdeljawad, Thabet, 2019. "On the oscillation of Caputo fractional differential equations with Mittag–Leffler nonsingular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 173-177.
    6. Mallika Arjunan, M. & Hamiaz, A. & Kavitha, V., 2021. "Existence results for Atangana-Baleanu fractional neutral integro-differential systems with infinite delay through sectorial operators," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    7. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    8. Asjad, Muhammad Imran & Sunthrayuth, Pongsakorn & Ikram, Muhammad Danish & Muhammad, Taseer & Alshomrani, Ali Saleh, 2022. "Analysis of non-singular fractional bioconvection and thermal memory with generalized Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    9. Owolabi, Kolade M. & Hammouch, Zakia, 2019. "Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1072-1090.
    10. Fetecau, C. & Zafar, A.A. & Vieru, D. & Awrejcewicz, J., 2020. "Hydromagnetic flow over a moving plate of second grade fluids with time fractional derivatives having non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    11. Ali, Farhad & Ali, Farman & Sheikh, Nadeem Ahmad & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2020. "Caputo–Fabrizio fractional derivatives modeling of transient MHD Brinkman nanoliquid: Applications in food technology," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    12. Riaz, M.B. & Iftikhar, N., 2020. "A comparative study of heat transfer analysis of MHD Maxwell fluid in view of local and nonlocal differential operators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    13. Rashid, Saima & Sultana, Sobia & Jarad, Fahd & Jafari, Hossein & Hamed, Y.S., 2021. "More efficient estimates via ℏ-discrete fractional calculus theory and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    14. Saad, Khaled M. & Srivastava, H.M. & Gómez-Aguilar, J.F., 2020. "A Fractional Quadratic autocatalysis associated with chemical clock reactions involving linear inhibition," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    15. Agarwal, Praveen & Singh, Ram, 2020. "Modelling of transmission dynamics of Nipah virus (Niv): A fractional order Approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    16. Kritika, & Agarwal, Ritu & Purohit, Sunil Dutt, 2020. "Mathematical model for anomalous subdiffusion using comformable operator," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    17. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    18. Partohaghighi, Mohammad & Akgül, Ali, 2021. "Modelling and simulations of the SEIR and Blood Coagulation systems using Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    19. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    20. ur Rahman, Ghaus & Agarwal, Ravi P. & Din, Qamar, 2019. "Mathematical analysis of giving up smoking model via harmonic mean type incidence rate," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 128-148.

    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:matcom:v:212:y:2023:i:c:p:224-233. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.