Abstract
A new fractional integral operator is used to present a generalized class of analytic functions in a complex domain. The method of definition is based on a Hadamard product of analytic function, which is called convolution product. Then we formulate a convolution integral operator acting on the sub-class of normalized analytic functions. Consequently, we investigate the suggested convolution operator geometrically. Differential subordination inequalities, taking the starlike formula are given. Some consequences of well-known results are illustrated.
Keywords: Analytic function, subordination and superordination, univalent function, open unit disk, fractional integral operator, convolution operator, fractional calculus.
Publisher
Babes-Bolyai University Cluj-Napoca
Reference33 articles.
1. "1. Agarwal, R.P., Luo, M.-J., Raina, R.K., On Ostrowski type inequalities, Fasc. Math.,
2. 56(2016), 5-27.
3. 2. Alazman, I., Ibrahim, R.W., Existence and uniqueness of fractal-fractional equations generated by a new fractal-fractional operator utilizing the advanced gamma function, MethodsX, 12(2024), 1-10.
4. 3. Al-Oboudi, F.M., On univalent functions defined by a generalized Sălăgean operator, Int.
5. J. Math. Math. Sci., 2004(2004), 1429-1436.