Geodesic
Iterated $g$-fractional vector representation formulae and inequalities for Banach space valued functions
Problemy analiza, Tome 9 (2020) no. 1, pp. 3-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Aliprantis C. D., Border K. C., Infinite Dimensional Analysis, Springer, New York, 2006 | MR | Zbl

[2] Anastassiou G. A., “Principles of General Fractional Analysis for Banach space valued functions”, Bulletin of Allahabad Math. Soc., 32:1 (2017), 71–145 | MR | Zbl

[3] Anastassiou G. A., Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations, Springer, Heidelberg–New York, 2018 | MR | Zbl

[4] Bochner integral, Encyclopedia of Mathematics, http://www.encyclopediaofmath.org/index.php?title=Bochner_integral&oldid=38659

[5] Kreuter M., Sobolev Space of Vector-valued functions, Master Thesis in Math., Ulm Univ., Ulm, Germany, 2015

[6] Mikkola K., Appendix B Integration and Differentiation in Banach Spaces, http://math.aalto.fi/k̃mikkola/research/thesis/contents/thesisb.pdf

[7] Mikusinski J., The Bochner integral, Academic Press, New York, 1978 | MR