ITERATED 𝐺-FRACTIONAL VECTOR REPRESENTATION FORMULAE AND INEQUALITIES FOR BANACH SPACE VALUED FUNCTIONS

Abstract

Here we present very general iterated fractional Bochner integral representation formulae for Banach space valued functions. Based on these we derive generalized and iterated left and right: fractional Poincar´e type inequalities, fractional Opial type inequalities and fractional Hilbert-Pachpatte inequalities. All these inequalities are very general having in their background Bochner type integrals.

Keywords

• banach space valued functions
• iterated vector generalized fractional derivative
• caputo fractional derivative
• iterated generalized vector fractional integral inequalities
• bochner integral
• fractional vector representation formulae