DOI QR코드

DOI QR Code

VECTORIAL HILFER-PRABHAKAR-HARDY TYPE FRACTIONAL INEQUALITIES

  • GEORGE A. ANASTASSIOU (Department of Mathematical Sciences, University of Memphis)
  • 투고 : 2023.04.28
  • 심사 : 2023.09.27
  • 발행 : 2023.11.30

초록

We present a variety of univariate and multivariate left and right side Hardy type fractional inequalities, many of them under convexity, and other also of Lp type, p ≥ 1, in the setting of generalized Hilfer and Prabhakar fractional Calculi.

키워드

참고문헌

  1. R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci. Numer. Simulat., 44 (2017), 460-481. https://doi.org/10.1016/j.cnsns.2016.09.006
  2. G.A. Anastassiou, Univariate Hardy-type fractional inequalities, Chapter 2, in "Advances in Applied Mathematics and Approximation Theory", Contributions from AMAT 2012, G. Anastassiou, O. Duman Editors, Springer, New York, 2013, pp. 21-56.
  3. G.A. Anastassiou, Intelligent Comparisons: Analytic Inequalities, Springer, Heidelberg, New York, 2016.
  4. G. Anastassiou, Advancements on ψ-Hilfer fractional calculus and fractional integral inequalities, Discontinuity, Nonlinear and Complexity accepted, 2021.
  5. G.A. Anastassiou, Foundations of Generalized Prabhakar-Hilfer fractional Calculus with Applications, Submitted, 2021.
  6. A. Giusti et al, A practical Guide to Prabhakar Fractional Calculus, Fractional Calculus & Applied Analysis 23 (2020), 9-54. https://doi.org/10.1515/fca-2020-0002
  7. R. Gorenflo, A. Kilbas, F. Mainardi, S. Rogosin, Mittag-Leffler functions, Related Topics and Applications, Springer, Heidelberg, New York, 2014.
  8. H.G. Hardy, Notes on some points in the integral calculus, Messenger of Mathematics 47 (1918), 145-150.
  9. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differentiation Equations, North Holland, Amsterdam, New York, 2006.
  10. F. Polito, Z. Tomovski, Some properties of Prabhakar-type fractional calculus operators, Fractional Differential Calculus 6 (2016), 73-94. https://doi.org/10.7153/fdc-06-05
  11. T.R. Prabhakar, A singular integral equation with a generalized Mittag Leffler function in the kernel, Yokohama Math. J. 19 (1971), 7-15.
  12. S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, Switzerland, 1993.
  13. Z. Tomovski, R. Hilfer, H.M. Srivastava, Fractional and Operational Calculus with Generalized Fractional Derivative Operators and Mittag-Leffler Type Functions, Integral Transforms Spec. Funct. 21 (2010), 797-814. https://doi.org/10.1080/10652461003675737
  14. J. Vanterler da C. Sousa, E. Capelas de Oliveira, On the ψ-Hilfer fractional derivative, Communications in Nonlinear Science and Numerical Simulation 60 (2018), 72-91.  https://doi.org/10.1016/j.cnsns.2018.01.005