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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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##### References:
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