Geodesic
Iterated $g$-fractional vector representation formulae and inequalities for Banach space valued functions
Problemy analiza, Tome 9 (2020) no. 1, pp. 3-26

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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. 
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     author = {George A. Anastassiou},
     title = {Iterated $g$-fractional vector representation formulae and inequalities for {Banach} space valued functions},
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     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2020_9_1_a0/}
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George A. Anastassiou. Iterated $g$-fractional vector representation formulae and inequalities for Banach space valued functions. Problemy analiza, Tome 9 (2020) no. 1, pp. 3-26. http://geodesic.mathdoc.fr/item/PA_2020_9_1_a0/