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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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