Time-space fractional heat equation in the unit disk. (English) Zbl 1291.35427

Ibrahim, Rabha W.; Jalab, Hamid A.

Abstr. Appl. Anal. 2013, Article ID 364042, 7 p. (2013).

Summary: We study a maximal solution of the time-space fractional heat equation in complex domain. The fractional time is taken in the sense of the Riemann-Liouville operator, while the fractional space is assumed in the Srivastava-Owa operator. Here we employ some properties of the univalent functions in the unit disk to determine the upper bound of this solution. The maximal solution is illustrated in terms of the generalized hypergeometric functions.

MSC:

35R11	Fractional partial differential equations
30C45	Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

References:

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