Evolution, its Fractional Extension and Generalization

Details Evolution, its Fractional Extension and Generalization Evolution, its Fractional Extension and Generalization

1999-12-29

arxiv.org/abs/math-ph/9912023v1

Physics

Mathematical Physics

10 pages, AMS-Tex

Scientific paper

The evolution of a quantity, described by a function of space and time, relates the first derivative in time of this function to a spatial operator applied to the function. The initial value of the function at time $t=0$ is given. The fractional extension of this evolution consists of replacing the first derivative in time by a fractional derivative of order $\alpha$, $0 < \alpha \le 1$. We give a relationship between the solution of the equation of evolution and the solution of the equation belonging to its fractional extension.

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