Tbilisi Mathematical Journal

Hardy-type inequalities for generalized fractional integral operators

Sajid Iqbal, Josip Pečarić, Muhammad Samraiz, and Živorad Tomovski

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Abstract

The aim of this research paper is to establish the Hardy-type inequalities for Hilfer fractional derivative and generalized fractional integral involving Mittag-Leffer function in its kernel using convex and increasing functions.

Article information

Source
Tbilisi Math. J., Volume 10, Issue 1 (2017), 75-90.

Dates
Received: 11 May 2015
Accepted: 14 June 2016
First available in Project Euclid: 26 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1527300018

Digital Object Identifier
doi:10.1515/tmj-2017-0005

Mathematical Reviews number (MathSciNet)
MR3607267

Zentralblatt MATH identifier
1358.26009

Subjects
Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 26D10: Inequalities involving derivatives and differential and integral operators 26A33: Fractional derivatives and integrals

Keywords
Hilfer fractional derivative Mittag-Leffer function Fractional integral

Citation

Iqbal, Sajid; Pečarić, Josip; Samraiz, Muhammad; Tomovski, Živorad. Hardy-type inequalities for generalized fractional integral operators. Tbilisi Math. J. 10 (2017), no. 1, 75--90. doi:10.1515/tmj-2017-0005. https://projecteuclid.org/euclid.tbilisi/1527300018


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References

  • Hardy GH. Notes on some points in the integral calculus, LX. An inequality between integrals. Messenger of Math. 1925;54:150-156.
  • Abramovich S, Kruli´c K, Pečarić J, Persson LE. Some new refined Hardy type inequalities with general kernels and measures. Aequationes Math. 2010;79:157-172.
  • Čižmešija A, Kruli\' c K, Pečarić J. Some new refined Hardy-type inequalities with kernels. J Math Inequal. 2010;4(4):481-503.
  • Čižmešija A, Kruli\' c K, Pečarić J. A new class of general refined Hardy-type inequality with kernels. Rad HAZU. 2013;17:53-80.
  • Farid G, Kruli´c K, Pe¡cari´c J. On refinement of Hardy type inequalities via superquadratic functions. Sarajevo J Math. 2011;7(20):163-175.
  • Iqbal S, Kruli\' c K, Pečarić J. On an inequality of H. G. Hardy. J Inequal Appl. Volume 2010:Article ID 264347.
  • Kruli\' c K, Pečarić J, Persson LE. Some new Hardy type inequalities with general kernels. Math Inequal Appl. 2009;12:473-485.
  • Niculescu C, Persson LE. Convex functions and their applications. A contemporary approach. CMC Books in Mathematics: Springer, New York; 2006.
  • Iqbal S, Kruli\' c K, Pečarić J. On an inequality for convex function with some applications on fractional derivatives and fractional integrals. J Math Inequal. 2011;5(2):219-230.
  • Kilbas AA, Srivastava HM, Trujillo JJ. Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204: Elsevier. New York-London; 2006.
  • Tomovski Ž, Hilfer R, Srivastava HM. Fractional and Operational Calculus with Generalized Fractional Derivative Operators and Mittag-Leffler Type Functions. Integral Transforms Spec Funct. 2010;21(11):797-814.
  • Hilfer R, Luchko Y, Tomovski Ž. Operational method for solution of fractional differential equations with generalized Riemann-Liouville fractional derivative. Fractional Calculus & Applied Analysis. 2009;12(3):299-318.
  • Kruli\' c K, Pečarić J, Pokaz D. Inequalities of Hardy and Jensen; 2013.
  • Salim TO, Faraj AW. A generalization of Mittag-Leffler function and integral operator associated with fractional calculus. JFCA. 2012;5:1-13.
  • Salim TO. Some properties relating to the generalized Mittag-Leffler function. Adv Appl Math Anal. 2009;4:21-30.
  • Shukla AK, Prajapati JC. On a generalization of Mittag-Leffler function and its properties. J Math Anal Appl. 2007;336:797-811.
  • Srivastava HM, Tomovski Z. Fractional calculus with an integral operator containing generalized Mittag-Leffler function in the kernal. Appl Math Comput. 2009;211:198-210.
  • Prabhakar TR. A Singular integral equation with a generalized Mittag-Leffler function in the kernel. Yokohama Math J. 1971;19:7-15.
  • Wiman A. Über den fundamentalsatz in der theorie der Funktionen. Acta Math. 1905;29:191-201.