IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2015y2015i1n746327.html

On the Nonlinear Perturbation K(n, m) Rosenau‐Hyman Equation: A Model of Nonlinear Scattering Wave

Author

Listed:
  • Abdon Atangana
  • Dumitru Baleanu
  • Maysaa’ Mohamed Al Qurashi
  • Xiao-Jun Yang

Abstract

We investigate a nonlinear wave phenomenon described by the perturbation K(n, m) Rosenau‐Hyman equation within the concept of derivative with fractional order. We used the Caputo fractional derivative and we proposed an iteration method in order to find a particular solution of the extended perturbation equation. We proved the stability and the convergence of the suggested method for solving the extended equation without any restriction on (m, n) and also on the perturbations terms. Using the inner product we proved the uniqueness of the special solution. By choosing randomly the fractional orders and m, we presented the numerical solutions.

Suggested Citation

  • Abdon Atangana & Dumitru Baleanu & Maysaa’ Mohamed Al Qurashi & Xiao-Jun Yang, 2015. "On the Nonlinear Perturbation K(n, m) Rosenau‐Hyman Equation: A Model of Nonlinear Scattering Wave," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:746327
    DOI: 10.1155/2015/746327
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2015/746327
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2015/746327?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. Carl M. Bender & Steven A. Orszag, 1999. "Advanced Mathematical Methods for Scientists and Engineers I," Springer Books, Springer, number 978-1-4757-3069-2, October.
    2. Abdon Atangana & Aydin Secer, 2013. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    3. Abdon Atangana & Aydin Secer, 2013. "A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    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. Abdon Atangana & Dumitru Baleanu, 2013. "Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yue Hu & Zuodong Yang, 2013. "Analytic Solution of a Class of Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Abdon Atangana & Necdet Bildik, 2013. "Approximate Solution of Tuberculosis Disease Population Dynamics Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Mubashir Qayyum & Sidra Nayab & Omar Khan, 2025. "Fuzzy-fractional modeling and analysis of virus propagation in wireless sensor networks via He-Laplace framework," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 88(2), pages 1-23, June.
    5. Guang-Sheng Chen & H. M. Srivastava & Pin Wang & Wei Wei, 2014. "Some Further Generalizations of Hölder′s Inequality and Related Results on Fractal Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Doungmo Goufo, Emile F. & Kumar, Sunil & Mugisha, S.B., 2020. "Similarities in a fifth-order evolution equation with and with no singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    8. Han, Huan & Wang, Zhanqing, 2019. "An alternating direction implicit scheme of a fractional-order diffusion tensor image registration model," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 105-118.
    9. Fendzi-Donfack, Emmanuel & Kenfack-Jiotsa, Aurélien, 2023. "Extended Fan’s sub-ODE technique and its application to a fractional nonlinear coupled network including multicomponents — LC blocks," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    10. Vázquez-Guerrero, P. & Gómez-Aguilar, J.F. & Santamaria, F. & Escobar-Jiménez, R.F., 2020. "Design of a high-gain observer for the synchronization of chimera states in neurons coupled with fractional dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    11. Doaa Atta & Ahmed E. Abouelregal & Fahad Alsharari, 2022. "Thermoelastic Analysis of Functionally Graded Nanobeams via Fractional Heat Transfer Model with Nonlocal Kernels," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    12. 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).
    13. Nuugulu, Samuel M & Gideon, Frednard & Patidar, Kailash C, 2021. "A robust numerical scheme for a time-fractional Black-Scholes partial differential equation describing stock exchange dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    14. Kumar, Sunil & Chauhan, R.P. & Momani, Shaher & Hadid, Samir, 2021. "A study of fractional TB model due to mycobacterium tuberculosis bacteria," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    15. Uddin, Md. Jasim & Rana, Sarker Md. Sohel & Işık, Seval & Kangalgil, Figen, 2023. "On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    16. Agarwal, Praveen & Singh, Ram & Rehman, Attiq ul, 2021. "Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam–Bashforth–Moulton predictor-corrector scheme," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    17. Gayathri Vivekanandan & Mahtab Mehrabbeik & Hayder Natiq & Karthikeyan Rajagopal & Esteban Tlelo-Cuautle, 2022. "Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns," Mathematics, MDPI, vol. 10(16), pages 1-9, August.
    18. Ram K. Saxena & Zivorad Tomovski & Trifce Sandev, 2015. "Analytical Solution of Generalized Space-Time Fractional Cable Equation," Mathematics, MDPI, vol. 3(2), pages 1-18, April.
    19. Yonkeu, R. Mbakob, 2023. "Stochastic bifurcations induced by Lévy noise in a fractional trirhythmic van der Pol system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    20. Abdon Atangana & Seyma Tuluce Demiray & Hasan Bulut, 2014. "Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    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:2015:y:2015:i:1:n:746327. 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.