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Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space

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  • Kangqun Zhang

Abstract

In this paper, we consider Cauchy problem of space-time fractional diffusion-wave equation. Applying Laplace transform and Fourier transform, we establish the existence of solution in terms of Mittag-Leffler function and prove its uniqueness in weighted Sobolev space by use of Mikhlin multiplier theorem. The estimate of solution also shows the connections between the loss of regularity and the order of fractional derivatives in space or in time.

Suggested Citation

  • Kangqun Zhang, 2020. "Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-6, February.
    • Handle: RePEc:hin:jnlamp:1545043
    DOI: 10.1155/2020/1545043
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