Poincaré Map for Discontinuous Fractional Differential Equations

Author:

Eliašová Ivana,Fečkan MichalORCID

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.

Funder

Slovak Research and Development Agency

Slovak Grant Agency VEGA

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference23 articles.

1. Di Bernardo, M. (2008). Piecewise-Smooth Dynamical Systems: Theory and Applications, Springer.

2. Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier Science.

3. Miller, K.S., and Ross, B. (1993). An Introduction to the Fractional Calculus and Differential Equations, John Wiley & Sons, Inc.

4. Olejnik, P., Awrejcewicz, J., and Fečkan, M. (2018). Modeling, Analysis and Control of Dynamical Systems: With Friction and Impacts, World Scientific Publishing Co. Pte. Ltd.

5. Podlubny, I. (1999). Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications, Academic Press.

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