Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side
In this paper we deal with the problem of asymptotic integration of a class of fractional differential equations of the Caputo type. The left-hand side of such type of equation is the Caputo derivative of the fractional order r ∈ (n − 1, n) of the solution, and the right-hand side depends not only...
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Vilnius Gediminas Technical University
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doaj-dca7d23008214bb6965fc85923ed353e2021-07-02T10:58:28ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102015-07-0120410.3846/13926292.2015.1068233Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand SideMilan Medved0Michal Pospisil1Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynska dolina, 842 48 Bratislava, SlovakiaCEITEC – Central European Institute of Technology, Brno University of Technology, Technicka 3058/10, 616 00 Brno, Czech Republic; Centre for Research and Utilization of Renewable Energy, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3058/10, 616 00 Brno, Czech Republic In this paper we deal with the problem of asymptotic integration of a class of fractional differential equations of the Caputo type. The left-hand side of such type of equation is the Caputo derivative of the fractional order r ∈ (n − 1, n) of the solution, and the right-hand side depends not only on ordinary derivatives up to order n − 1 but also on the Caputo derivatives of fractional orders 0 < r1 < · · · < rm < r, and the Riemann–Liouville fractional integrals of positive orders. We give some conditions under which for any global solution x(t) of the equation, there is a constant c ∈ R such that x(t) = ctR + o(tR) as t → ∞, where R = max{n − 1, rm}. https://journals.vgtu.lt/index.php/MMA/article/view/1014Caputo fractional derivativenonlinear equationasymptotic propertydesingularization |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Milan Medved Michal Pospisil |
spellingShingle |
Milan Medved Michal Pospisil Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side Mathematical Modelling and Analysis Caputo fractional derivative nonlinear equation asymptotic property desingularization |
author_facet |
Milan Medved Michal Pospisil |
author_sort |
Milan Medved |
title |
Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side |
title_short |
Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side |
title_full |
Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side |
title_fullStr |
Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side |
title_full_unstemmed |
Asymptotic Integration of Fractional Differential Equations with Integrodifferential Right-Hand Side |
title_sort |
asymptotic integration of fractional differential equations with integrodifferential right-hand side |
publisher |
Vilnius Gediminas Technical University |
series |
Mathematical Modelling and Analysis |
issn |
1392-6292 1648-3510 |
publishDate |
2015-07-01 |
description |
In this paper we deal with the problem of asymptotic integration of a class of fractional differential equations of the Caputo type. The left-hand side of such type of equation is the Caputo derivative of the fractional order r ∈ (n − 1, n) of the solution, and the right-hand side depends not only on ordinary derivatives up to order n − 1 but also on the Caputo derivatives of fractional orders 0 < r1 < · · · < rm < r, and the Riemann–Liouville fractional integrals of positive orders. We give some conditions under which for any global solution x(t) of the equation, there is a constant c ∈ R such that x(t) = ctR + o(tR) as t → ∞, where R = max{n − 1, rm}.
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topic |
Caputo fractional derivative nonlinear equation asymptotic property desingularization |
url |
https://journals.vgtu.lt/index.php/MMA/article/view/1014 |
work_keys_str_mv |
AT milanmedved asymptoticintegrationoffractionaldifferentialequationswithintegrodifferentialrighthandside AT michalpospisil asymptoticintegrationoffractionaldifferentialequationswithintegrodifferentialrighthandside |
_version_ |
1721331609300369408 |