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The fractional diffusion equation. (English) Zbl 0632.35031
In one space - and in one time-dimension a diffusion equation is solved, where the first time derivative is replaced by the $$\lambda$$-fractional time derivative, $$0<\lambda \leq 1$$. The solution is given in closed form interms of Fox functions.

##### MSC:
 35K57 Reaction-diffusion equations 26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems 35C05 Solutions to PDEs in closed form
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##### References:
 [1] Fox C., Trans. Am. Math. Soc. 98 pp 395– (1961) [2] Braaksma B. L. S., Compos. Math. 15 pp 239– (1964) [3] Gupta K. G., Proc. Nat. Acad. Sci. India A 36 pp 594– (1966) [4] DOI: 10.1002/pssb.2221330150
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