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

Rabha W. Ibrahim^1, and Hamid A. Jalab²

¹Institute of Mathematical Sciences, University Malaya, 50603, Malaysia

²Faculty of Computer Science and Information Technology, University, Malaya, 50603, Malaysia

Cite this paper:
Rabha W. Ibrahim and Hamid A. Jalab. Studies on Fractional Differential Operators of Two Parameters in a Complex Domain. Turkish Journal of Analysis and Number Theory. 2016; 4(1):1-7. doi: 10.12691/tjant-4-1-1

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.

Keywords:
Fractional calculus fractional differential operator fractional differential equation analytic function

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