Periodicity of a time-delay system of fractional order joining n-deviating arguments

ABSTRACT

In this study, we generalize a time-delay system joining n-deviating arguments by utilizing the concept of the Riemann–Liouville fractional calculus. The class of equations is taken in view of the Rayleigh-type equation. Our tool is based on the fixed-point theorems. The existence of the outcomes is delivered under some certain conditions. The application is illustrated in the sequel.

KEYWORDS:

• Rayleigh equation
• fractional calculus
• fractional differential equations
• periodic solution

Authors' contributions

The authors jointly worked on deriving the results and approved the final manuscript.

Acknowledgments

The authors thank the referees for giving useful suggestions for improving the work.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCiD

R.W. Ibrahim http://orcid.org/0000-0001-9341-025X