FRACTIONAL CALCULUS BETWEEN BANACH SPACES ALONG WITH OSTROWSKI AND GR\"{U}SS TYPE INEQUALITIES

Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 93

Volume : 10 , Issue : 1
DOI: https://doi.org/10.56827/JRSMMS.2022.1001.2
Author :
George A. Anastassiou (Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.)

Abstract

Here we present a fractional calculus Caputo type for functions between Banach spaces. Left and right fractional derivatives are defined on a segment of a Banach space, then we expand. We apply the above to new Ostrowski and Gr\"{u}ss type inequalities at very abstract level.

Keywords and Phrases

Abstract fractional calculus, abstract fractional derivative, Ostrowski inequality, Gr\"{u}ss inequality.

A.M.S. subject classification

26A33, 26D10, 26D15.

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