Publication detail

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

ŘEHÁK, P.

Original Title

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

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

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

Authors

ŘEHÁK, P.

Released

6. 11. 2023

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Location

OXFORD

ISBN

0893-9659

Periodical

APPLIED MATHEMATICS LETTERS

Year of study

145

Number

108779

State

United States of America

Pages from

1

Pages to

9

Pages count

9

URL

https://www.sciencedirect.com/science/article/pii/S0893965923002112

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)",
  journal="APPLIED MATHEMATICS LETTERS",
  year="2023",
  volume="145",
  number="108779",
  pages="1--9",
  doi="10.1016/j.aml.2023.108779",
  issn="0893-9659",
  url="https://www.sciencedirect.com/science/article/pii/S0893965923002112"
}