Shigeyoshi OWA, Neslihan UYANIK

Some applications of fractional calculus for analytic function

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

For analytic functions f (z) in the class An, fractional calculus (fractional integrals and fractional derivatives) D λ z f (z) of order λ are introduced. Applying D λ z f (z) for f (z) ∈ An, we introduce the interesting subclass An (αm, β, ρ, λ) of An. The object of this paper is to discuss some properties of f (z) concerning D λ z f (z).

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[1] Jack IS. Functions starlike and convex of order α. Journal of the London Mathematical Society 1971; 3: 469-474.
[2] Miller SS, Mocanu PT. Second-order differential inequalities in the complex plane. Journal of Mathematical Analysis and Applications 1978; 65: 289-305.
[3] Miller SS, Mocanu PT. Differential Subordinations: Theory and Applications. New York, NY, USA: Marcel Dekker Incorporated, 2000.
[4] Owa S. On the distortion theorems-I. Kyungpook Mathematical Journal 1978; 18: 53-59.
[5] Owa S. On applications of the fractional calculus. Mathematica Japonica 1980; 25: 195-206.
[6] Owa S, Srivastava HM. Univalent and starlike generalized hypergeometric functions. Canadian Journal of Mathematics 1987; 39: 1067-1077.