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Strong Mixed and Generalized Abstract Fractional Calculus

  • George A. Anastassiou
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 734)

Abstract

We present here a strong mixed fractional calculus theory for Banach space valued functions of generalized Canavati type. Then we establish several mixed fractional Bochner integral inequalities of various types. It follows Anastassiou (Mat Vesn Accept, [5]).

References

  1. 1.
    R.P. Agarwal, V. Lupulescu, D. O’Regan, G. Rahman, Multi-term fractional differential equations in a nonreflexive Banach space. Adv. Differ. Equ. 2013, 302 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    C.D. Aliprantis, K.C. Border, Infinite Dimensional Analysis (Springer, New York, 2006)zbMATHGoogle Scholar
  3. 3.
    G.A. Anastassiou, Intelligent Comparisons: Analytic Inequalities (Springer, New York, 2016)CrossRefzbMATHGoogle Scholar
  4. 4.
    G.A. Anastassiou, Strong right fractional calculus for banach space valued functions. Rev. Proyecciones 36(1), 149–186 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    G.A. Anastassiou, Strong mixed and generalized Fractional Calculus for Banach space valued functions. Mat. Vesn. (2016) (Accepted)Google Scholar
  6. 6.
    G.A. Anastassiou, A strong Fractional Calculus Theory for Banach space valued functions. Nonlinear Funct. Anal. Appl. (2017) (Accepted)Google Scholar
  7. 7.
    F. Appendix, The Bochner Integral and Vector-valued \(L_{p}\) -spaces, https://isem.math.kit.edu/images/f/f7/AppendixF.pdf
  8. 8.
  9. 9.
    J.A. Canavati, The Riemann-Liouville integral. Nieuw Archief Voor Wiskunde 5(1), 53–75 (1987)MathSciNetzbMATHGoogle Scholar
  10. 10.
    M. Kreuter, Sobolev Spaces of Vector-valued functions. Ulm University, Master Thesis in Mathematics, Ulm, Germany (2015)Google Scholar
  11. 11.
    J. Mikusinski, The Bochner Integral (Academic Press, New York, 1978)CrossRefzbMATHGoogle Scholar
  12. 12.
    G.E. Shilov, Elementary Functional Analysis (Dover Publications Inc, New York, 1996)zbMATHGoogle Scholar
  13. 13.
    C. Volintiru, A proof of the fundamental theorem of Calculus using Hausdorff measures. R. Anal. Exch. 26(1), 381–390 (2000/2001)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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