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Wirtinger-type inequalities for Caputo fractional derivatives via Taylor's formula
(Springer, 2024) Erden, Samet; Sarikaya, Mehmet Zeki; Ozdemir, Burcin Gokkurt; Uyanik, Neslihan
In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional Taylor's Formulas. Afterward, we provide a more general inequality involving Caputo fractional derivatives for L-r norm with r>1 via Holder's inequality. Also, similar inequalities for Riemann-Liouville fractional derivatives are presented by means of a relation between Caputo fractional derivatives and Riemann-Liouville fractional derivatives.