A Class of Symmetric Fractional Differential Operator Formed by Special Functions

Abstract

In light of a certain sort of fractional calculus, a generalized symmetric fractional differential operator based on Raina’s function is built. The generalized operator is then used to create a formula for analytic functions of type normalized. We use the ideas of subordination and superordination to show a collection of inequalities using the suggested differential operator. The new Raina’s operator is also used to the generalized kinematic solutions (GKS). Using the concepts of subordination and superordination, we provide analytic solutions for GKS. As a consequence, a certain hypergeometric function provides the answer. A fractional coefficient differential operator is also created. The geometric and analytic properties of the object are being addressed. The symmetric differential operator in a complex domain is shown to be a generalized fractional differential operator. Finally, we explore the characteristics of the Raina’s symmetric differential operator.