IDEAS home Printed from https://ideas.repec.org/a/wly/jnlamp/v2015y2015i1n719173.html

Spatial Rotation of the Fractional Derivative in Two‐Dimensional Space

Author

Listed:
  • Ehab Malkawi

Abstract

The transformations of the partial fractional derivatives under spatial rotation in R2 are derived for the Riemann‐Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed through fractional derivatives, with respect to different coordinate systems (observers). It is the hope that such understanding could shed light on the physical interpretation of fractional derivatives. Also it is necessary to be able to construct interaction terms that are invariant with respect to equivalent observers.

Suggested Citation

  • Ehab Malkawi, 2015. "Spatial Rotation of the Fractional Derivative in Two‐Dimensional Space," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:719173
    DOI: 10.1155/2015/719173
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2015/719173
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2015/719173?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. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
    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. Ochoa-Tapia, J. Alberto & Valdes-Parada, Francisco J. & Alvarez-Ramirez, Jose, 2007. "A fractional-order Darcy's law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 1-14.
    2. Owolabi, Kolade M., 2016. "Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 89-98.
    3. Hejazi, S. Reza & Saberi, Elaheh & Mohammadizadeh, Fatemeh, 2021. "Anisotropic non-linear time-fractional diffusion equation with a source term: Classification via Lie point symmetries, analytic solutions and numerical simulation," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    4. Owolabi, Kolade M., 2020. "High-dimensional spatial patterns in fractional reaction-diffusion system arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Wang, Yiduan & Zheng, Shenzhou & Zhang, Wei & Wang, Guochao & Wang, Jun, 2018. "Fuzzy entropy complexity and multifractal behavior of statistical physics financial dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 486-498.
    6. Bolster, Diogo & Benson, David A. & Meerschaert, Mark M. & Baeumer, Boris, 2013. "Mixing-driven equilibrium reactions in multidimensional fractional advection–dispersion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2513-2525.
    7. Liang, Yanming & Guo, Yongfeng & Lin, Zifei & Kapitaniak, Tomasz, 2026. "Synchronization and chimera dynamics in fractional-order FitzHugh-Nagumo neuronal networks with fractal connectivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 685(C).
    8. Adán J. Serna-Reyes & Jorge E. Macías-Díaz & Nuria Reguera, 2021. "A Convergent Three-Step Numerical Method to Solve a Double-Fractional Two-Component Bose–Einstein Condensate," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    9. Vasily E. Tarasov, 2021. "General Fractional Vector Calculus," Mathematics, MDPI, vol. 9(21), pages 1-87, November.
    10. Che, Han & Wang, Yu-Lan & Li, Zhi-Yuan, 2022. "Novel patterns in a class of fractional reaction–diffusion models with the Riesz fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 149-163.
    11. Troparevsky, M.I. & Muszkats, J.P. & Seminara, S.A. & Zitto, M.E. & Piotrkowski, R., 2022. "Modeling particulate pollutants dispersed in the atmosphere using fractional turbulent diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    12. Cai, Rui-Yang & Cheng, Lan & Zhou, Hua-Cheng, 2024. "Sliding mode control for the stabilization of fractional heat equations subject to boundary uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    13. Prodanov, Dimiter, 2016. "Characterization of strongly non-linear and singular functions by scale space analysis," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 14-19.

    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:719173. 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.