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In this paper, first we obtain some inequalities of Hadamard type for $(h-m)-$convex functions via Caputo $k-$fractional derivatives. Secondly, two integral identities including the $(n+1)$ and $(n+2)$ order derivatives of a given function via Caputo $k-$fractional derivatives have been established. Using these identities estimations of Hadamard type integral inequalities for the Caputo $k-$fractional derivatives have been proved.
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참고문헌 신청
F. Chen / 2014 / On Hermite-Hadamard type inequalities for Riemann-Liouville frac-tional integrals via two kinds of convexity / Chin. J. Math :7
G. Farid / 2017 / On Hadamard inequalities for n-times differentiable functions which are relative convex via Caputo k-fractional deriva-tives / Nonlinear Anal. Forum 22(2):17~28
G. Farid / 2016 / On Hadamard inequalities for k-fractional integrals / Nonlinear Funct. Anal. Appl 21(3):463~478
R. Goreno / 1997 / Fractional calculus: Integral and differential equa-tions of fractional order / Springer Verlag
A. A. Kilbas / 2006 / Theory and applications of fractional differential equations / Elsevier
G. Farid / 2017 / On Hadamard inequalities for n-times differentiable functions which are relative convex via Caputo k-fractional deriva-tives / Nonlinear Anal. Forum 22(2):17~28
G. Farid / 2016 / On Hadamard inequalities for k-fractional integrals / Nonlinear Funct. Anal. Appl 21(3):463~478
R. Goreno / 1997 / Fractional calculus: Integral and differential equa-tions of fractional order / Springer Verlag
A. A. Kilbas / 2006 / Theory and applications of fractional differential equations / Elsevier
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