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

Recommended by Vladimir Mityushev

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.