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Subordination and superordination for univalent solutions for fractional differential equations. (English) Zbl 1147.30009
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.
MSC:
30C45Special classes of univalent and multivalent functions
26A33Fractional derivatives and integrals (real functions)
References:
[1]Goodman, A. W.: Univalent function, (1983)
[2]Srivastava, H. M.; Owa, S.: Univalent functions, fractional calculus, and their applications, (1989)
[3]Podlubny, I.: Fractional differential equations, (1999)
[4]Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations, (1993)
[5]Oldham, K. B.; Spanier, J.: The fractional calculus, Math. sci. Eng. (1974)
[6]Balachandar, K.; Dauer, J. P.: Elements of control theory, (1999)
[7]Curtain, R. F.; Pritchard, A. J.: Functional analysis in modern applied mathematics, (1977)
[8]Samko, S. G.; Kilbas, A. A.; Marichev, O. I.: Fractional integrals and derivatives (Theory and applications), (1993) · Zbl 0818.26003
[9]Miller, S. S.; Mocanu, P. T.: Subordinants of differential superordinations, Complex variables 48, No. 10, 815-826 (2003) · Zbl 1039.30011 · doi:10.1080/02781070310001599322
[10]Miller, S. S.; Mocanu, P. T.: Differential subordinations: theory and applications, Pure appl. Math. 225 (2000) · Zbl 0954.34003
[11]Shanmugam, T. N.; Ravichangran, V.; Sivasubramanian, S.: Differential sandwich theorems for some subclasses of analytic functions, Aust. math, anal. Appl. 3, No. 1, 1-11 (2006) · Zbl 1091.30019
[12]Bulboaca, T.: Classes of first-order differential superordinations, Demonstratio math. 35, No. 2, 287-292 (2002) · Zbl 1010.30020
[13]Kiryakova, V.: Generalized fractional calculus and applications, Pitman res. Notes math. Ser. 301 (1994) · Zbl 0882.26003