New Results on (r,k,μ)-Riemann–Liouville Fractional Operators in Complex Domain with Applications
Adel Salim Tayyah, Waggas Galib Atshan
Abstract
This paper introduces fractional operators in the complex domain as generalizations for the Srivastava–Owa operators. Some properties for the above operators are also provided. We discuss the convexity and starlikeness of the generalized Libera integral operator. A condition for the convexity and starlikeness of the solutions of fractional differential equations is provided. Finally, a fractional differential equation is converted into an ordinary differential equation by wave transformation; illustrative examples are provided to clarify the solution within the complex domain.
Topics & Concepts
MathematicsDomain (mathematical analysis)Fractional calculusRiemann hypothesisPure mathematicsMathematical physicsMathematical analysisDifferential Equations and Boundary ProblemsAnalytic and geometric function theoryNonlinear Differential Equations Analysis