Advances in Mathematical Physics (Jan 2020)

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

  • Kangqun Zhang

DOI
https://doi.org/10.1155/2020/1545043
Journal volume & issue
Vol. 2020

Abstract

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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.