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Fractional-order diffusion-wave equation. (English) Zbl 0846.35001
Summary: The fractional-order diffusion-wave equation is an evolution equation of order \(\alpha\in (0, 2]\) which continues to the diffusion equation when \(\alpha\to 1\) and to the wave equation when \(\alpha\to 2\). We prove some properties of its solution and give some examples. We define a new fractional calculus (negative-direction fractional calculus) and study some of its properties. We study the existence, uniqueness, and properties of the solution of the negative-direction fractional diffusion-wave problem.

MSC:
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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