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

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.)
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### References:

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