On The ( k , s )‐Hilfer Fractional Derivatives via Wirtinger‐Type Inequalities and Their Analytical Applications

Key Points

• This research aims to define Hilfer fractional derivatives and explore their properties through inequalities.
• Introduced a novel definition of Hilfer fractional derivative.
• Established fractional Wirtinger-type inequalities using Hölder's inequality.
• Presented special cases and graphical examples to illustrate main results.
• Demonstrated new fractional inequalities applicable in different mathematical contexts.
• Provided examples that validate the significance of the established inequalities.
• Applied inequalities to illustrate connections between arithmetic and geometric means.

Abstract