Detail publikace

Superlinear solutions of sublinear fractional differential equations and regular variation

ŘEHÁK, P.

Originální název

Superlinear solutions of sublinear fractional differential equations and regular variation

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

ŘEHÁK, P.

Vydáno

24. 4. 2023

Nakladatel

Springer Nature

Místo

LONDON

ISSN

1311-0454

Periodikum

Fractional Calculus and Applied Analysis

Ročník

26

Číslo

1

Stát

Bulharská republika

Strany od

989

Strany do

1015

Strany počet

27

URL

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

Plný text v Digitální knihovně

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"
}