Superlinear solutions of sublinear fractional differential equations and regular variation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F23%3APU148187" target="_blank" >RIV/00216305:26210/23:PU148187 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s13540-023-00156-1" target="_blank" >https://link.springer.com/article/10.1007/s13540-023-00156-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13540-023-00156-1" target="_blank" >10.1007/s13540-023-00156-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Superlinear solutions of sublinear fractional differential equations and regular variation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Superlinear solutions of sublinear fractional differential equations and regular variation

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/GA20-11846S" target="_blank" >GA20-11846S: Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fractional Calculus and Applied Analysis

ISSN

1311-0454

e-ISSN

1314-2224

Svazek periodika

26

Číslo periodika v rámci svazku

2023

Stát vydavatele periodika

BG - Bulharská republika

Počet stran výsledku

27

Strana od-do

989-1015

Kód UT WoS článku

000973087600001

EID výsledku v databázi Scopus

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