Studies on Fractional Differential Operators of Two Parameters in a Complex Domain

Abstract

This study deals with a generalization for fractional differential operators in a complex domain based on the extended Beta function. Stipulations are imposed for these generalized operators such as the upper bounds. Other possessions for the above operator are also prepared. In addition, implementations of these operators are introduced and suggested in the geometric function theory (GFT). Sufficient conditions are imposed for functions to be univalent.

On simple iterative fractional order differential equations

“…We popularize and extends the classic model based on the concept of fractional calculus and the most befitting formula is the iterative fractional integral and differential equations. Many authors have studied this area including (see [1,2,3,4,5,6,7,8,9,10]). The first work in this field was that of E, Eder [11] in 1984, which gave the existence and unique solutions of equation w (τ) = w(w(τ))…”

“…Finally, the Extremal solutions were proven by monotone iterative technique for hybrid fractional differential equations using theorem Dhage fixed point [10].…”