IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v140y2020ics0960077920305956.html
   My bibliography  Save this article

Mathematical model for anomalous subdiffusion using comformable operator

Author

Listed:
  • Kritika,
  • Agarwal, Ritu
  • Purohit, Sunil Dutt

Abstract

In the present work, we investigate the calcium signaling in cardiac myocytes. On the basis of the concept of anomalous diffusion, a mathematical model is proposed to characterize the anomalous subdiffusion of cytosolic calcium incorporating conformable derivative with respect to the time variable and fractal derivative with respect to the space variable. Problem has been solved using the Crank-Nicolson finite difference scheme for numerical approximation. The numerical simulation for the solution of the developed model is presented graphically for the various values of the fractal dimension and order of the fractional derivative.

Suggested Citation

  • Kritika, & Agarwal, Ritu & Purohit, Sunil Dutt, 2020. "Mathematical model for anomalous subdiffusion using comformable operator," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305956
    DOI: 10.1016/j.chaos.2020.110199
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920305956
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110199?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. Kanno, Ryutaro, 1998. "Representation of random walk in fractal space-time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 248(1), pages 165-175.
    2. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. 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.
    4. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    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. Shyamsunder, & Bhatter, S. & Jangid, Kamlesh & Purohit, S.D., 2022. "Fractionalized mathematical models for drug diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    2. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

    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. 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.
    2. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Ahmad, Shabir & Ullah, Aman & Arfan, Muhammad & Shah, Kamal, 2020. "On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana-Baleanu (AB) derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Kucche, Kishor D. & Sutar, Sagar T., 2021. "Analysis of nonlinear fractional differential equations involving Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Owolabi, Kolade M. & Karaagac, Berat, 2020. "Dynamics of multi-pulse splitting process in one-dimensional Gray-Scott system with fractional order operator," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    6. Owolabi, Kolade M. & Pindza, Edson, 2019. "Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 146-157.
    7. Fawaz E. Alsaadi & Amirreza Yasami & Christos Volos & Stelios Bekiros & Hadi Jahanshahi, 2023. "A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy," Mathematics, MDPI, vol. 11(2), pages 1-25, January.
    8. Pritam, Kocherlakota Satya & Sugandha, & Mathur, Trilok & Agarwal, Shivi, 2021. "Underlying dynamics of crime transmission with memory," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Mahmood, Tariq & ur Rahman, Mati & Arfan, Muhammad & Kayani, Sadaf-Ilyas & Sun, Mei, 2023. "Mathematical study of Algae as a bio-fertilizer using fractal–fractional dynamic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 207-222.
    10. Singh, C.S. & Singh, Harendra & Singh, Somveer & Kumar, Devendra, 2019. "An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1440-1448.
    11. 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).
    12. Ullah, Ihsan & Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "Investigation of fractional order tuberculosis (TB) model via Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    13. Suwan, Iyad & Abdeljawad, Thabet & Jarad, Fahd, 2018. "Monotonicity analysis for nabla h-discrete fractional Atangana–Baleanu differences," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 50-59.
    14. 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).
    15. Chimmula, Vinay Kumar Reddy & Zhang, Lei, 2020. "Time series forecasting of COVID-19 transmission in Canada using LSTM networks," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    16. Mahmoud, Emad E. & Trikha, Pushali & Jahanzaib, Lone Seth & Almaghrabi, Omar A., 2020. "Dynamical analysis and chaos control of the fractional chaotic ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    17. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    18. Etemad, Sina & Avci, Ibrahim & Kumar, Pushpendra & Baleanu, Dumitru & Rezapour, Shahram, 2022. "Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    19. Chatibi, Y. & El Kinani, E.H. & Ouhadan, A., 2019. "Variational calculus involving nonlocal fractional derivative with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 117-121.
    20. Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.

    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:140:y:2020:i:c:s0960077920305956. 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.