JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2024, no.1, 2024 (SCI-Expanded)
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.