Detail publikačního výsledku

Existence of positive periodic solutions of some nonlinear fractional differential equations

CABADA, A.; KISELA, T.

Originální název

Existence of positive periodic solutions of some nonlinear fractional differential equations

Anglický název

Existence of positive periodic solutions of some nonlinear fractional differential equations

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

CABADA, A.; KISELA, T.

Rok RIV

2018

Vydáno

01.09.2017

Nakladatel

Elsevier Science BV

Místo

Amsterdam, Netherlands

ISSN

1007-5704

Periodikum

Communications in Nonlinear Science and Numerical Simulation

Svazek

50

Číslo

1

Stát

Nizozemsko

Strany od

51

Strany do

67

Strany počet

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"
}