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Mellin integral transform approach to analyze the multidimensional diffusion-wave equations

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  • Boyadjiev, Lyubomir
  • Luchko, Yuri

Abstract

In this paper, a family of the multidimensional time- and space-fractional diffusion-wave equations with the Caputo time-fractional derivative of the order β, 0 < β ⩽ 2 and the fractional Laplacian (−Δ)α2 with 1 < α ⩽ 2 is considered. A representation of the first fundamental solution to this equation is deduced in form of a Mellin–Barnes integral by employing the technique of the Mellin integral transform. The Mellin–Barnes representation is used to derive some new identities for the fundamental solutions in different dimensions and to identify already known and some new particular cases of the fundamental solution that have especially simple closed form.

Suggested Citation

  • Boyadjiev, Lyubomir & Luchko, Yuri, 2017. "Mellin integral transform approach to analyze the multidimensional diffusion-wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 127-134.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:127-134
    DOI: 10.1016/j.chaos.2017.03.050
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    References listed on IDEAS

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    1. Al-Refai, Mohammed & Luchko, Yuri, 2015. "Maximum principle for the multi-term time-fractional diffusion equations with the Riemann–Liouville fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 40-51.
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    Cited by:

    1. Yuri Luchko, 2019. "Some Schemata for Applications of the Integral Transforms of Mathematical Physics," Mathematics, MDPI, vol. 7(3), pages 1-18, March.
    2. Ansari, Alireza & Derakhshan, Mohammad Hossein, 2023. "On spectral polar fractional Laplacian," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 636-663.
    3. Emilia Bazhlekova & Ivan Bazhlekov, 2019. "Subordination Approach to Space-Time Fractional Diffusion," Mathematics, MDPI, vol. 7(5), pages 1-12, May.
    4. Yuri Luchko, 2017. "On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation," Mathematics, MDPI, vol. 5(4), pages 1-16, December.
    5. repec:eur:ejfejr:65 is not listed on IDEAS
    6. Awad, Emad & Sandev, Trifce & Metzler, Ralf & Chechkin, Aleksei, 2021. "Closed-form multi-dimensional solutions and asymptotic behaviors for subdiffusive processes with crossovers: I. Retarding case," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    7. Francesco Mainardi & Armando Consiglio, 2020. "The Wright Functions of the Second Kind in Mathematical Physics," Mathematics, MDPI, vol. 8(6), pages 1-26, June.

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