Superlinear solutions of sublinear fractional differential equations and regular variation
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Superlinear solutions of sublinear fractional differential equations and regular variation
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10100 - Mathematics
Result continuities
Project
<a href="/en/project/GA20-11846S" target="_blank" >GA20-11846S: Differential and difference equations of real orders: Qualitative analysis and its applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fractional Calculus and Applied Analysis
ISSN
1311-0454
e-ISSN
1314-2224
Volume of the periodical
26
Issue of the periodical within the volume
2023
Country of publishing house
BG - BULGARIA
Number of pages
27
Pages from-to
989-1015
UT code for WoS article
000973087600001
EID of the result in the Scopus database
—