Strong right fractional calculus for Banach space valued functions
DOI:
https://doi.org/10.4067/S0716-09172017000100009Keywords:
Right Fractional derivative, Right Fractional Taylor’s formula, Banach space valued functions, integral inequalities, Hausdorff measure, Bochner integralAbstract
We present here a strong right fractional calculus theory for Banach space valued functions of Caputo type. Then we establish many right fractional Bochner integral inequalities of various types.References
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[2] C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, Springer, New York, (2006).
[3] G. Anastassiou, Fractional Differentiation Inequalities, Springer, New York, (2009).
[4] G. Anastassiou, Advances on fractional inequalities, Springer, New York, (2011).
[5] Appendix F, The Bochner integral and vector-valued Lp-spaces, https://isem.math.kit.edu/images/f/f7/AppendixF.pdf.
[6] Bochner integral. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bochner integral&oldid=38659.
[7] R.F. Curtain and A.J. Pritchard, Functional Analysis in Modern Applied Mathematics, Academic Press, London, New York, (1977).
[8] M. Kreuter, Sobolev Spaces of Vector-valued functions, Ulm Univ., Master Thesis in Math., Ulm, Germany, (2015).
[9] E. Landau, Einige Ungleichungen f¨ ur zweimal differentzierban funktionen, Proc. London Math. Soc. 13, pp. 43-49, (1913).
[10] J. Mikusinski, The Bochner integral, Academic Press, New York, (1978).
[11] G.E. Shilov, Elementary Functional Analysis, Dover Publications, Inc., New York, (1996).
[12] C. Volintiru, A proof of the fundamental theorem of Calculus using Hausdorff measures, Real Analysis Exchange, 26 (1), 2000/2001, pp. 381-390.
Published
2017-04-06
How to Cite
[1]
G. A. Anastassiou, “Strong right fractional calculus for Banach space valued functions”, Proyecciones (Antofagasta, On line), vol. 36, no. 1, pp. 149-186, Apr. 2017.
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