IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v130y2020ics0960077919303315.html
   My bibliography  Save this article

Numerical analysis of a new volterra integro-differential equation involving fractal-fractional operators

Author

Listed:
  • ARAZ, Seda İĞRET

Abstract

In this paper, we suggest a new integro-differential equation by utilizing from the concept of fractal-fractional derivative and integral newly introduced by Atangana. We offer that under which conditions the solution of the suggested equation is exist and unique benefitting from Banach fixed-point theorem. Also, we construct a new numerical scheme for the numerical solution of our problem and we give numerical simulation and illustrations for different values of fractional order α and fractal order β. That’s why, this study will guide for researchers significantly in theory and applications.

Suggested Citation

  • ARAZ, Seda İĞRET, 2020. "Numerical analysis of a new volterra integro-differential equation involving fractal-fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303315
    DOI: 10.1016/j.chaos.2019.109396
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919303315
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.109396?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. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    2. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    3. Murat SUBASI & Seda Igret ARAZ & Hakki GUNGOR, 2017. "On the Numerical Solution of Two Dimensional Schrodinger Equation," International Journal of Mathematics Research, Conscientia Beam, vol. 6(1), pages 1-12.
    4. Atangana, Abdon, 2018. "Blind in a commutative world: Simple illustrations with functions and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 347-363.
    5. Atangana, Abdon & Alqahtani, Rubayyi T., 2018. "New numerical method and application to Keller-Segel model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 14-21.
    6. Murat SUBAŞI & Seda İğret ARAZ & Hakkı GÜNGÖR, 2017. "On the Numerical Solution of Two Dimensional Schrodinger Equation," International Journal of Mathematical Research, Conscientia Beam, vol. 6(1), pages 1-12.
    7. Atangana, Ernestine, 2019. "New insight kinetic modeling: Models above classical chemical mechanic," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 16-24.
    8. Chen, W., 2006. "Time–space fabric underlying anomalous diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 923-929.
    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. Omaba, McSylvester Ejighikeme, 2021. "Growth moment, stability and asymptotic behaviours of solution to a class of time-fractal-fractional stochastic differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. 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).
    4. Zhang, Yonghong & Mao, Shuhua & Kang, Yuxiao & Wen, Jianghui, 2021. "Fractal derivative fractional grey Riccati model and its application," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Shojaeizadeh, T. & Mahmoudi, M. & Darehmiraki, M., 2021. "Optimal control problem of advection-diffusion-reaction equation of kind fractal-fractional applying shifted Jacobi polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. He, Jing & Mao, Shuhua & Kang, Yuxiao, 2023. "Augmented fractional accumulation grey model and its application: Class ratio and restore error perspectives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 220-247.
    7. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(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. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Imran, M.A., 2020. "Application of fractal fractional derivative of power law kernel (FFP0Dxα,β) to MHD viscous fluid flow between two plates," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Shojaeizadeh, T. & Mahmoudi, M. & Darehmiraki, M., 2021. "Optimal control problem of advection-diffusion-reaction equation of kind fractal-fractional applying shifted Jacobi polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Li, Zhongfei & Liu, Zhuang & Khan, Muhammad Altaf, 2020. "Fractional investigation of bank data with fractal-fractional Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Babu, N. Ramesh & Balasubramaniam, P., 2022. "Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Saifullah, Sayed & Ali, Amir & Franc Doungmo Goufo, Emile, 2021. "Investigation of complex behaviour of fractal fractional chaotic attractor with mittag-leffler Kernel," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Ahmad, Shabir & Ullah, Aman & Akgül, Ali, 2021. "Investigating the complex behaviour of multi-scroll chaotic system with Caputo fractal-fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. Rashid, Saima & Jarad, Fahd & Alsharidi, Abdulaziz Khalid, 2022. "Numerical investigation of fractional-order cholera epidemic model with transmission dynamics via fractal–fractional operator technique," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    10. Xuan, Liu & Ahmad, Shabir & Ullah, Aman & Saifullah, Sayed & Akgül, Ali & Qu, Haidong, 2022. "Bifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    11. Khan, Hasib & Gómez-Aguilar, J.F. & Khan, Aziz & Khan, Tahir Saeed, 2019. "Stability analysis for fractional order advection–reaction diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 737-751.
    12. Ahmad, Zubair & Ali, Farhad & Khan, Naveed & Khan, Ilyas, 2021. "Dynamics of fractal-fractional model of a new chaotic system of integrated circuit with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    13. Babu, N. Ramesh & Balasubramaniam, P., 2023. "Master–slave synchronization for glucose–insulin metabolism of type-1 diabetic Mellitus model based on new fractal–fractional order derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 282-301.
    14. Zhang, Tianxian & Zhao, Yongqi & Xu, Xiangliang & Wu, Si & Gu, Yujuan, 2024. "Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    15. Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    16. Shloof, A.M. & Senu, N. & Ahmadian, A. & Salahshour, Soheil, 2021. "An efficient operation matrix method for solving fractal–fractional differential equations with generalized Caputo-type fractional–fractal derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 415-435.
    17. Tassaddiq, Asifa, 2019. "MHD flow of a fractional second grade fluid over an inclined heated plate," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 341-346.
    18. Sina Etemad & Albert Shikongo & Kolade M. Owolabi & Brahim Tellab & İbrahim Avcı & Shahram Rezapour & Ravi P. Agarwal, 2022. "A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability," Mathematics, MDPI, vol. 10(22), pages 1-31, November.
    19. Akgül, Ali & Siddique, Imran, 2021. "Analysis of MHD Couette flow by fractal-fractional differential operators," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    20. Li, Xiao-Ping & Din, Anwarud & Zeb, Anwar & Kumar, Sunil & Saeed, Tareq, 2022. "The impact of Lévy noise on a stochastic and fractal-fractional Atangana–Baleanu order hepatitis B model under real statistical data," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

    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:130:y:2020:i:c:s0960077919303315. 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.