Publication detail

Existence of positive periodic solutions of some nonlinear fractional differential equations

CABADA, A. KISELA, T.

Original Title

Existence of positive periodic solutions of some nonlinear fractional differential equations

Type

journal article in Web of Science

Language

English

Original Abstract

The paper is devoted to study of existence and uniqueness of periodic solutions for a particular class of nonlinear fractional differential equations admitting its right-hand side with certain singularities. Our approach is based on Krasnosel'ski\u{\i} and Schauder fixed point theorems and monotone iterative technique which enable us to extend some previously known results. The discussed problems are characterized by a Green's function which has integrable singularities disallowing a direct use of classical techniques known from theory of ordinary differential equations, therefore proper modifications are proposed. Furher, the paper presents simple numerical algorithms directly built on the iterative technique used in theoretical proofs. Illustrative examples conclude the paper.

Keywords

Periodic Fractional Equation; Krasnoselskii fixed point; Green's function; Monotone Iterative Methods

Authors

CABADA, A.; KISELA, T.

Released

1. 9. 2017

Publisher

Elsevier Science BV

Location

Amsterdam, Netherlands

ISBN

1007-5704

Periodical

Communications in Nonlinear Science and Numerical Simulation

Year of study

50

Number

1

State

Kingdom of the Netherlands

Pages from

51

Pages to

67

Pages count

17

BibTex

@article{BUT132972,
  author="Alberto {Cabada} and Tomáš {Kisela}",
  title="Existence of positive periodic solutions of some nonlinear fractional differential equations",
  journal="Communications in Nonlinear Science and Numerical Simulation",
  year="2017",
  volume="50",
  number="1",
  pages="51--67",
  doi="10.1016/j.cnsns.2017.02.010",
  issn="1007-5704"
}