On Coefficient Bounds for Analytic Functions Associated with a Generalized Fractional Differential Operator
Smrutirekha Patra
Department of Mathematics, School of Sciences, Gandhi Institute of Engineering and Technology University, Gunupur, Rayagada-765022, Odisha, India.
Sasmita Nag
Department of Mathematics, School of Sciences, Gandhi Institute of Engineering and Technology University, Gunupur, Rayagada-765022, Odisha, India.
Rupali Sahu
Department of Mathematics, School of Sciences, Gandhi Institute of Engineering and Technology University, Gunupur, Rayagada-765022, Odisha, India.
Laxmipriya Parida *
Department of Mathematics, School of Sciences, Gandhi Institute of Engineering and Technology University, Gunupur, Rayagada-765022, Odisha, India.
*Author to whom correspondence should be addressed.
Abstract
In the present paper, we investigate sharp coefficient estimates for several newly defined subclasses of analytic functions associated with the generalized fractional differential operator \(D^{v,n}_\lambda\). By applying techniques from differential subordination theory, we derive upper bounds for the initial Taylor coefficients |\(a_2\)|, |\(a_3\)|, |\(a_4\)| and |\(a_5\)| for the classes \(S^{v,n}_\lambda\) (\(\eta\)), \(C^{v,n}_\lambda\) (\(\eta, [\psi]\)) and \(R^{v,n}_\lambda\) (\(\eta,\gamma, [\psi]\)). The results obtained extend and improve a number of previously known bounds due to Sharma et al. (2016), Bansal (2013), Raza and Malik (2013), and others. In addition, several special cases and consequences are discussed. These results significantly contribute to the ongoing development of geometric function theory involving fractional operators and provide a unified approach to coefficient inequalities for analytic functions in the open unit disk.
Keywords: Analytic functions, fractional differential operator, coefficient estimates, univalent functions, subordination