This article is cited in 2 papers

Iterated $g$-fractional vector representation formulae and inequalities for Banach space valued functions

George A. Anastassiou

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

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 Poincaré 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.

UDC: 517.28, 517.98, 517.444

MSC: 26A33, 26B40, 26D10, 26D15, 46B25, 46E40

Received: 19.11.2019
Revised: 29.12.2019
Accepted: 09.01.2020

Language: English

DOI: 10.15393/j3.art.2020.7630

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