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New function of Mittag–Leffler type and its application in the fractional diffusion-wave equation

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  • Yu, Rui
  • Zhang, Hongqing

Abstract

The classical Mittag–Leffler (M–L) functions have already proved their efficiency as solutions of fractional-order differential and integral equations. In this paper we introduce a modified M–L type function and deduce its important integral transforms. Then the solution of the initial-boundary value problem for the so-called fractional diffusion-wave equation with real-order time and space derivatives is given by using the inverse Fourier transform of the new function.

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  • Yu, Rui & Zhang, Hongqing, 2006. "New function of Mittag–Leffler type and its application in the fractional diffusion-wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 946-955.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:4:p:946-955
    DOI: 10.1016/j.chaos.2005.08.151
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    Cited by:

    1. Gafiychuk, V. & Datsko, B. & Meleshko, V. & Blackmore, D., 2009. "Analysis of the solutions of coupled nonlinear fractional reaction–diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1095-1104.

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