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Generalised fractional evolution equations of Caputo type

Author

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  • Hernández-Hernández, M.E.
  • Kolokoltsov, V.N.
  • Toniazzi, L.

Abstract

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions. These results encompass known linear and non-linear equations from classical fractional partial differential equations such as the time-space-fractional diffusion equation, as well as their far reaching extensions.

Suggested Citation

  • Hernández-Hernández, M.E. & Kolokoltsov, V.N. & Toniazzi, L., 2017. "Generalised fractional evolution equations of Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 184-196.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:184-196
    DOI: 10.1016/j.chaos.2017.05.005
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    References listed on IDEAS

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    1. Chakrabarty, Arijit & Meerschaert, Mark M., 2011. "Tempered stable laws as random walk limits," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 989-997, August.
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    Cited by:

    1. González Cázares, Jorge Ignacio & Lin, Feng & Mijatović, Aleksandar, 2025. "Fast exact simulation of the first-passage event of a subordinator," Stochastic Processes and their Applications, Elsevier, vol. 183(C).

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