Eur. Phys. J. Special Topics 226, 3681–3692 (2017)
https://doi.org/10.1140/epjst/e2018-00017-9

Regular Article

Approximation approach to periodic BVP for fractional differential systems

¹ Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
² Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
³ Department of Differential Equations and Mathematical Physics, Uzhhorod National University, Narodna Square, 3, Uzhhorod 88000, Ukraine

^a e-mail: michal.feckan@gmail.com

Received: 18 May 2017
Received in final form: 14 November 2017
Published online: 25 July 2018

Abstract

We give a new approach of investigation and approximation of solutions of fractional differential systems (FDS) subjected to periodic boundary conditions. According to the main idea of the numerical–analytic technique, we construct a sequence of functions that it proved to be convergent. It is shown that the limit function of the constructed sequence satisfies a modified FDS and periodic conditions. It is a solution of the given periodic BVP, if the corresponding determined equation has a root. An example of fractional Duffing equation is also presented to illustrate the theory.