Poincaré Map for Discontinuous Fractional Differential Equations

Abstract

We work with a perturbed fractional differential equation with discontinuous right-hand sides where a discontinuity function crosses a discontinuity boundary transversally. The corresponding Poincaré map in a neighbourhood of a periodic orbit of an unperturbed equation is found. Then, bifurcations of periodic boundary solutions are analysed together with a concrete example.

Keywords

• fractional differential equation
• periodic boundary condition
• discontinuous system
• Poincaré map
• bifurcations