New Results on <inline-formula><math display="inline"><semantics><mrow><mo mathvariant="bold">(</mo><mi mathvariant="bold-italic">r</mi><mo mathvariant="bold">,</mo><mi mathvariant="bold-italic">k</mi><mo mathvariant="bold">,</mo><mi mathvariant="bold-italic">μ</mi><mo mathvariant="bold">)</mo></mrow></semantics></math></inline-formula>-Riemann–Liouville Fractional Operators in Complex Domain with Applications

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.

Keywords

• Riemann-Liouville fractional operators
• Caputo derivative
• fractional differential equations
• convex and starlike functions
• fractional complex transform
• Mittag-Leffler function