Poincaré Map for Discontinuous Fractional Differential Equations

Ivana Eliašová and Michal Fečkan ()
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Ivana Eliašová: Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská Dolina, 842 48 Bratislava, Slovakia
Michal Fečkan: Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská Dolina, 842 48 Bratislava, Slovakia

Mathematics, 2022, vol. 10, issue 23, 1-16

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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