zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

30C45Special classes of univalent and multivalent functions
26A33Fractional derivatives and integrals (real functions)
Full Text: DOI
[1] Goodman, A. W.: Univalent function, (1983)
[2] Srivastava, H. M.; Owa, S.: Univalent functions, fractional calculus, and their applications, (1989) · Zbl 0683.00012
[3] Podlubny, I.: Fractional differential equations, (1999) · Zbl 0924.34008
[4] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equations, (1993) · Zbl 0789.26002
[5] Oldham, K. B.; Spanier, J.: The fractional calculus, Math. sci. Eng. (1974) · Zbl 0292.26011
[6] Balachandar, K.; Dauer, J. P.: Elements of control theory, (1999) · Zbl 0965.93002
[7] Curtain, R. F.; Pritchard, A. J.: Functional analysis in modern applied mathematics, (1977) · Zbl 0448.46002
[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