Sobolev, Hardy, Gagliardo–Nirenberg, and Caffarelli–Kohn–Nirenberg-type inequalities for some fractional derivatives
Kassymov A. Ruzhansky M. Tokmagambetov N. Torebek B.T.
1 January 2021Birkhauser
Banach Journal of Mathematical Analysis
2021#15Issue 1
In this paper, we show different inequalities for fractional-order differential operators. In particular, the Sobolev, Hardy, Gagliardo–Nirenberg, and Caffarelli–Kohn–Nirenberg-type inequalities for the Caputo, Riemann–Liouville, and Hadamard derivatives are obtained. In addition, we show some applications of these inequalities.
Caffarelli–Kohn–Nirenberg inequality , Caputo derivative , fractional-order differential operator , Gagliardo–Nirenberg inequality , Hadamard derivative , Hardy inequality , Riemann–Liouville derivative , Sobolev inequality
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Al-Farabi Kazakh National University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
School of Mathematical Sciences
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
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