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In this article, we establish some new weighted Hardy-type inequalities involving some variants of extended Riemann-Liouville fractional derivative operators, using convex and increasing functions. As special cases of the main results, we obtain the results of \cite{spp, s1}. We also prove the boundedness of the $k$-fractional integral operator on $L_{p}[a,b]$.
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참고문헌 (33)
참고문헌 신청
N. Abel / 2012 / Oeuvres completes de Niels Henrik Abel: Nouvelle edition (Cambridge Library Collection - Mathematics) / Cambridge University Press :11~27
E. Adeleke / 2012 / On a new class of Hardy-type inequalities / J. Inequal. Appl 2012:259~277
M. Ali Ozarslan / 2010 / Some generating relations for extended hypergeometric functions via generalized fractional derivative operator / Math. Comput. Modelling 52(9-10):1825~1833
G. A. Anastassiou / 2009 / Fractional differentiation inequalities / Springer
D. Baleanu / 2017 / Extension of the fractional derivative operator of the Riemann-Liouville / J. Nonlinear Sci. Appl 10(6):2914~2924
E. Adeleke / 2012 / On a new class of Hardy-type inequalities / J. Inequal. Appl 2012:259~277
M. Ali Ozarslan / 2010 / Some generating relations for extended hypergeometric functions via generalized fractional derivative operator / Math. Comput. Modelling 52(9-10):1825~1833
G. A. Anastassiou / 2009 / Fractional differentiation inequalities / Springer
D. Baleanu / 2017 / Extension of the fractional derivative operator of the Riemann-Liouville / J. Nonlinear Sci. Appl 10(6):2914~2924
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