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

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
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    3. 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.
    4. 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.
    5. 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.
    6. 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.
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