IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v515y2019icp403-418.html
   My bibliography  Save this article

The fractional space–time radial diffusion equation in terms of the Fox’s H-function

Author

Listed:
  • Costa, F.S.
  • Oliveira, D.S.
  • Rodrigues, F.G.
  • de Oliveira, E.C.

Abstract

Based on a generalization of the Hilfer–Katugampola fractional operator, recently introduced, and the Weyl fractional derivative, which are responsible to describe the memory and distance effects, respectively, we investigate the anomalous diffusion in processes in which fractional radial differential equation plays an important and fundamental rule. Similarity solutions for this fractional space–time radial equation are considered. These solutions are presented in terms of the Fox’s H-function. As an application, we present and discuss a special case in fractal Hausdorff dimension.

Suggested Citation

  • Costa, F.S. & Oliveira, D.S. & Rodrigues, F.G. & de Oliveira, E.C., 2019. "The fractional space–time radial diffusion equation in terms of the Fox’s H-function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 403-418.
    • Handle: RePEc:eee:phsmap:v:515:y:2019:i:c:p:403-418
    DOI: 10.1016/j.physa.2018.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118313396
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.10.002?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. S. P. Mahulikar & H. Herwig, 2008. "Fluid friction in incompressible laminar convection: Reynolds' analogy revisited for variable fluid properties," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(1), pages 77-86, March.
    2. Verma, S. & Viswanathan, P., 2018. "A note on Katugampola fractional calculus and fractal dimensions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 220-230.
    3. Jun-Sheng Duan & Ai-Ping Guo & Wen-Zai Yun, 2014. "Similarity Solution for Fractional Diffusion Equation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, March.
    4. Sun, HongGuang & Hao, Xiaoxiao & Zhang, Yong & Baleanu, Dumitru, 2017. "Relaxation and diffusion models with non-singular kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 590-596.
    5. Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Reyes-Reyes, J. & Adam-Medina, M., 2016. "Modeling diffusive transport with a fractional derivative without singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 467-481.
    6. Alkahtani, B.S.T. & Atangana, A., 2016. "Controlling the wave movement on the surface of shallow water with the Caputo–Fabrizio derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 539-546.
    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. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Numerical approximation of nonlinear fractional parabolic differential equations with Caputo–Fabrizio derivative in Riemann–Liouville sense," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 171-179.
    2. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    3. Al-Refai, Mohammed & Jarrah, Abdulla M., 2019. "Fundamental results on weighted Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 7-11.
    4. Yu, Xiangnan & Zhang, Yong & Sun, HongGuang & Zheng, Chunmiao, 2018. "Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: Analytical solution in bounded-domain and model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 306-312.
    5. Xu, Xuefang & Li, Bo & Qiao, Zijian & Shi, Peiming & Shao, Huaishuang & Li, Ruixiong, 2023. "Caputo-Fabrizio fractional order derivative stochastic resonance enhanced by ADOF and its application in fault diagnosis of wind turbine drivetrain," Renewable Energy, Elsevier, vol. 219(P1).
    6. Owolabi, Kolade M. & Atangana, Abdon, 2018. "Chaotic behaviour in system of noninteger-order ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 362-370.
    7. Shuai Yang & Qing Wei & Lu An, 2022. "Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository," Mathematics, MDPI, vol. 10(14), pages 1-7, July.
    8. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 111-119.
    9. Cuahutenango-Barro, B. & Taneco-Hernández, M.A. & Gómez-Aguilar, J.F., 2018. "On the solutions of fractional-time wave equation with memory effect involving operators with regular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 283-299.
    10. Lei, Dong & Liang, Yingjie & Xiao, Rui, 2018. "A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 465-475.
    11. Owolabi, Kolade M., 2017. "Mathematical modelling and analysis of two-component system with Caputo fractional derivative order," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 544-554.
    12. Tian, Xue & Zhang, Yi, 2019. "Noether’s theorem for fractional Herglotz variational principle in phase space," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 50-54.
    13. Abro, Kashif Ali & Abro, Irfan Ali & Yıldırım, Ahmet, 2020. "A comparative analysis of sulfate SO4−2 ion concentration via modern fractional derivatives: An industrial application to cooling system of power plant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    14. Sun, HongGuang & Hao, Xiaoxiao & Zhang, Yong & Baleanu, Dumitru, 2017. "Relaxation and diffusion models with non-singular kernels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 590-596.
    15. Ding, Juan-Juan & Zhang, Yi, 2020. "Noether’s theorem for fractional Birkhoffian system of Herglotz type with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    16. Avcı, Derya & Yetim, Aylin, 2019. "Cauchy and source problems for an advection-diffusion equation with Atangana–Baleanu derivative on the real line," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 361-365.
    17. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 285-294.
    18. Liu, Zhengguang & Cheng, Aijie & Li, Xiaoli, 2017. "A second order Crank–Nicolson scheme for fractional Cattaneo equation based on new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 361-374.
    19. Cai, Rui-Yang & Zhou, Hua-Cheng & Kou, Chun-Hai, 2021. "Boundary control strategy for three kinds of fractional heat equations with control-matched disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    20. Zhao, Dazhi & Luo, Maokang, 2019. "Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 531-544.

    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:phsmap:v:515:y:2019:i:c:p:403-418. 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/physica-a-statistical-mechpplications/ .

    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.