Hilbert–Pachpatte type general integral inequalities

Abstract

In this article we present very general weighted Hilbert–Pachpatte type integral inequalities. These are regarding ordinary derivatives and fractional derivatives of Riemann–Liouiville and Canavati types. Also regarding general derivatives of Widder type and linear differential operators. Our results apply to continuous functions and some to integrable functions.

Keywords:

• Hilbert inequality
• Hilbert–Pachpatte inequality
• Hölder inequalities
• Fractional derivatives
• Linear differential operator

Keywords:

• AMS 2000 Mathematics Subject Classifications:
• 26A33
• 26D10
• 26D15