International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 153280, 10 pages
doi:10.1155/2008/153280
Research Article

Second Hankel Determinant for a Class of Analytic Functions Defined by Fractional Derivative

A. K. Mishra and P. Gochhayat

Department of Mathematics, Berhampur University, Bhanja Bihar, Berhampur 760 007, Orissa, India

Received 4 April 2007; Accepted 21 November 2007

Academic Editor: Vladimir Mityushev

Copyright © 2008 A. K. Mishra and P. Gochhayat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By making use of the fractional differential operator Ωzλ due to Owa and Srivastava, a class of analytic functions ℛλ(α,ρ)    (0≤ρ≤1,  0≤λ<1,    |α|<π/2) is introduced. The sharp bound for the nonlinear functional |a2a4−a32| is found. Several basic properties such as inclusion, subordination, integral transform, Hadamard product are also studied.