Riemann-Liouville derivative over the space of integrable distributions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114386" target="_blank" >RIV/00216224:14310/20:00114386 - isvavai.cz</a>
Result on the web
<a href="http://www.aimsciences.org/article/doi/10.3934/era.2020030" target="_blank" >http://www.aimsciences.org/article/doi/10.3934/era.2020030</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/era.2020030" target="_blank" >10.3934/era.2020030</a>
Alternative languages
Result language
angličtina
Original language name
Riemann-Liouville derivative over the space of integrable distributions
Original language description
In this paper, we generalize the Riemann-Liouville differential and integral operators on the space of Henstock-Kurzweil integrable distributions, DHK. We obtain new fundamental properties of the fractional derivatives and integrals, a general version of the fundamental theorem of fractional calculus, semigroup property for the Riemann-Liouville integral operators and relations between the Riemann-Liouville integral and differential operators. Also, we achieve a generalized characterization of the solution for the Abel integral equation. Finally, we show relations for the Fourier transform of fractional derivative and integral. These results are based on the properties of the distributional Henstock-Kurzweil integral and convolution.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-03224S" target="_blank" >GA17-03224S: Asymptotic theory of ordinary and fractional differential equations and their numerical discretizations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Research Archive
ISSN
2688-1594
e-ISSN
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Volume of the periodical
28
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
567-587
UT code for WoS article
000544123800001
EID of the result in the Scopus database
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