Subordination and superordination for univalent solutions for fractional differential equations. (English) Zbl 1147.30009

Ibrahim, Rabha W.; Darus, Maslina

J. Math. Anal. Appl. 345, No. 2, 871-879 (2008).

In this paper the authors establish the existence and uniqueness of univalent solutions for fractional differential equations. The existence is obtained by applying the Schauder fixed point theorem while the uniqueness is obtained by the Banach fixed point theorem. Also some properties of this solution involving fractional differential subordination are given.

Reviewer: Tej Singh Nahar (Bhilwara)

MSC:

30C45	Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
26A33	Fractional derivatives and integrals

Keywords:

fractional calculus; analytic function

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