Publication detail

Superlinear solutions of sublinear fractional differential equations and regular variation

ŘEHÁK, P.

Original Title

Superlinear solutions of sublinear fractional differential equations and regular variation

Type

journal article in Web of Science

Language

English

Original Abstract

We consider a sublinear fractional equation of the order in the interval (1, 2). We give conditions guaranteeing that this equation possesses asymptotically superlinear solutions. We show that all of these solutions are regularly varying and establish precise asymptotic formulae for them. Further we prove non-improvability of the conditions. In addition to the asymptotically superlinear solutions we discuss also other classes of solutions, some of them having no ODE analogy. In the very special case, when the coefficient is asymptotically equivalent to a power function and the order of the equation is 2, we get known results in their full generality. We reveal substantial differences between the integer order and non-integer order case. Among other tools, we utilize the fractional Karamata integration theorem and the fractional generalized L'Hospital rule which are proved in the paper. Several examples illustrating our results but serving also in alternative proofs are given too. We provide also numerical simulations.

Keywords

Sublinear fractional differential equation; Asymptotically superlinear solution; Regularly varying function; Karamata theorem; Asymptotic formula

Authors

ŘEHÁK, P.

Released

24. 4. 2023

Publisher

Springer Nature

Location

LONDON

ISBN

1311-0454

Periodical

Fractional Calculus and Applied Analysis

Year of study

26

Number

1

State

Republic of Bulgaria

Pages from

989

Pages to

1015

Pages count

27

URL

https://link.springer.com/article/10.1007/s13540-023-00156-1

Full text in the Digital Library

http://hdl.handle.net/11012/213670

BibTex

@article{BUT183583,
  author="Pavel {Řehák}",
  title="Superlinear solutions of sublinear fractional differential equations and regular variation",
  journal="Fractional Calculus and Applied Analysis",
  year="2023",
  volume="26",
  number="1",
  pages="989--1015",
  doi="10.1007/s13540-023-00156-1",
  issn="1311-0454",
  url="https://link.springer.com/article/10.1007/s13540-023-00156-1"
}