Detail publikace

On decaying and asymptotically constant solutions of nonlinear equations with the Weyl fractional derivative of an order in (1,2)

ŘEHÁK, P.

Anglický název

On decaying and asymptotically constant solutions of nonlinear equations with the Weyl fractional derivative of an order in (1,2)

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

We consider a sublinear fractional differential equation of an order in the interval (1,2) where the fractional derivative is of the Weyl type. Existence and asymptotic behavior of decaying and asymptotically constant positive solutions is studied. We mainly deal with regularly varying coefficients and/or solutions, but we also allow a more general setting. Our results are sharp and in the special case where the coefficient in the equation is asymptotically equivalent to a power function and the order of the equation is 2 we get back known results. An important role in the proofs is played by the fractional Karamata integration theorem and other properties of regularly varying functions, fixed point principle, and generalized fractional L'Hospital rule.& COPY; 2023 Elsevier Ltd. All rights reserved.

Anglický abstrakt

We consider a sublinear fractional differential equation of an order in the interval (1,2) where the fractional derivative is of the Weyl type. Existence and asymptotic behavior of decaying and asymptotically constant positive solutions is studied. We mainly deal with regularly varying coefficients and/or solutions, but we also allow a more general setting. Our results are sharp and in the special case where the coefficient in the equation is asymptotically equivalent to a power function and the order of the equation is 2 we get back known results. An important role in the proofs is played by the fractional Karamata integration theorem and other properties of regularly varying functions, fixed point principle, and generalized fractional L'Hospital rule.& COPY; 2023 Elsevier Ltd. All rights reserved.

Klíčová slova anglicky

Sublinear fractional differential; equation; Weyl fractional integral; Decaying solution; Regularly varying function; Karamata theorem; Asymptotic formula

Vydáno

06.11.2023

Nakladatel

PERGAMON-ELSEVIER SCIENCE LTD

Místo

OXFORD

ISSN

0893-9659

Ročník

145

Číslo

108779

Strany od–do

1–9

Počet stran

9

BIBTEX


@article{BUT185079,
  author="Pavel {Řehák},
  title="On decaying and asymptotically constant solutions of nonlinear equations with the Weyl fractional derivative of an order in (1,2)",
  year="2023",
  volume="145",
  number="108779",
  month="November",
  pages="1--9",
  publisher="PERGAMON-ELSEVIER SCIENCE LTD",
  address="OXFORD",
  issn="0893-9659"
}