Estimating Coefficient Bounds for Classes of Bi-univalent Functions Defined by Fractional Derivatives

Let \(f(z)=z+\sum _{k=n}^{\infty }a_k z^k;(n\ge 2)\) be a bi-univalent function in the unit disk \(\mathbb {U}=\{z:\;|z|<1\})\) . We investigate bounds of \(|a_{n}|\) , \(|a_{2n-1}|\) , \(|a_{2n-1}-na_n^2|\) and \(|a_{2n-1}-a_n^2|\) for classes of bi-univalent functions defined by fractional derivatives. The results include generalizations and improvements for well known estimates.