Kolmogorov type inequalities for Hadamard fractional derivatives of functions defined on half-line, and their applications

V.F. Babenko; N.V. Parfinovich; A.A. Semirenko

doi:10.15421/241207

Kolmogorov type inequalities for Hadamard fractional derivatives of functions defined on half-line, and their applications

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0001-6677-1914
N.V. Parfinovich (Oles Honchar Dnipropetrovsk National University)
A.A. Semirenko (Oles Honchar Dnipropetrovsk National University)

Abstract

For the norms of fractional Hadamard derivatives of functions defined on the half-line, the sharp Kolmogorov-type inequalities are obtained. Applications of these inequalities are given.

Keywords

fractional derivative; sharp inequality; norm; function

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References

Arestov V.V. "Approximation of unbounded operators by the bounded ones and related extremum problems", Uspekhi mat. nauk, 1996; 51(6): pp. 88-124. (in Russian) doi:10.1070/RM1996v051n06ABEH003001

Arestov V.V., Gabushin V.N. "The best approximation of unbounded operators by the bounded ones", Izv. vuzov. Matematika, 1995; 11: pp. 42-63. (in Russian)

Babenko V.F., Korneichuk N.P., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Naukova dumka, Kyiv, 2003; 590 p. (in Russian)

Babenko V.F., Parfinovich N.V. "On inequalities of Kolmogorov type for Hadamard fractional derivatives of functions defined on half-line", Res. Math., 2009; 17(6/1): pp. 31-35. (in Russian)

Babenko V.F., Parfinovich N.V. "Sharp inequalities of Kolmogorov type for Hadamard fractional derivatives of functions defined on half-line", Res. Math., 2010; 18(6/1): pp. 38-48. (in Russian)

Babenko V.F., Churilova M.S. "On inequalities of Kolmogorov type for derivatives of fractional order", Res. Math., 2001; 6: pp. 16-20. (in Russian)

Babenko V.F., Churilova M.S. "Estimates for norms of fractional derivatives by integral moduli of continuity and their applications", Ukrainian Math. J., 2011; 63(9): pp. 1155-1168. (in Russian) doi:10.1007/s11253-012-0581-9

Motornyi V.P., Babenko V.F., Dovgoshej A.A., Kuznetsova O.I. Approximation theory and Fourier analysis, Naukova dumka, Kyiv, 2010; 302 p. (in Russian)

Samko S.G., Kilbas A.A., Marichev O.I. Integrals and derivatives of fractional order and their applications, Minsk, 1987; 688 p. (in Russian)

Stechkin S.B. "The best approximation of linear operators", Matem. zametki, 1967; 1(2): pp. 137-148. (in Russian) doi:10.1007/BF01268056