Very recently, a new local and KYO-DOPHILUS limit-based extension of derivatives, called conformable derivative, has been formulated.We define a new conformable derivative in the complex domain, derive its differential calculus properties as well as its geometric properties in the field of geometric function theory.In addition, we employ the new conformable operator to generalize the Briot-Bouquet differential equation.
We establish analytic solutions for the generalized Briot-Bouquet differential equation by using the Shirts concept of subordination and superordination.Examples of special normalized functions are illustrated in the sequel.