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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 140, Pages 68–77 (Mi into235)  
Inequalities involving fractional integrals of a function and its derivative

R. G. Nasibullin

Kazan (Volga Region) Federal University
Full-text PDF (189 kB)
Abstract: New inequalities for fractional integrals of a function and its derivative are proved. Lower estimates of weighted norms of the derivative through fractional Riemann–Liouville integrals are obtained.
Keywords: Hardy inequality, fractional Riemann–Liouville integral, Bessel function.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00351-а
15-41-02433
This work was supported by the Russian Foundation for Basic Research (project No. 14-01-00351-a) and the joint grant of the Russian Foundation for Basic Research and the Government of the Republic of Tatarstan No. 15-41-02433.
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 4, Pages 448–457
DOI: https://doi.org/10.1007/s10958-019-04436-1
Bibliographic databases:
Document Type: Article
UDC: 517.5, 517.956.225
MSC: 26D15, 46E30
Language: Russian
Citation: R. G. Nasibullin, “Inequalities involving fractional integrals of a function and its derivative”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 140, VINITI, M., 2017, 68–77; Journal of Mathematical Sciences, 241:4 (2019), 448–457
Citation in format AMSBIB
\Bibitem{Nas17}
\by R.~G.~Nasibullin
\paper Inequalities involving fractional integrals of a function and its derivative
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 140
\pages 68--77
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into235}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3799896}
\zmath{https://zbmath.org/?q=an:1426.26037}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 4
\pages 448--457
\crossref{https://doi.org/10.1007/s10958-019-04436-1}
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