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Hardy’s Type Inequalities via Conformable Calculus

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Frontiers in Functional Equations and Analytic Inequalities

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Abstract

In this chapter, we establish some inequalities of Hardy and Leindler type and their converses via conformable calculus with weighted functions. As applications, we obtain some classical integral inequalities as special cases.

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References

  1. T. Abdeljawad, On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)

    Article  MathSciNet  Google Scholar 

  2. A. Akkurt, M.E. Yildirim, H. Yildirim, On some integral inequalities for conformable fractional integrals. RGMIA Res. Rep. Collection 19, 107, 8pp. (2016)

    Google Scholar 

  3. M.U. Awan, M.A. Noor, T.S. Du, K.I. Noor, New refinements of fractional Hermite–Hadamard inequality. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. https://doi.org/10.1007/s13398-017-0448-x

  4. K. Bogdan, B. Dyda, The best constant in a fractional Hardy inequality. Math. Nach. 284, 629–638 (2011)

    Article  MathSciNet  Google Scholar 

  5. E.T. Copson, Note on series of positive terms. J. Lond. Math. Soc. 3, 49–51 (1928)

    Article  MathSciNet  Google Scholar 

  6. Y.M. Chu, M.A. Khan, T. Ali, S.S. Dragomir, Inequalities for α-fractional differentiable functions. J. Inequal Appl. 1, 93 (2017)

    Article  MathSciNet  Google Scholar 

  7. G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, 2nd edn. (Cambridge University Press, Cambridge, 1952)

    MATH  Google Scholar 

  8. M. Jleli, B. Samet, Lyapunov-type inequalities for a fractional differential equation with mixed boundary conditions. Math. Inequal. Appl. 18, 443–451 (2015)

    MathSciNet  MATH  Google Scholar 

  9. R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)

    Article  MathSciNet  Google Scholar 

  10. M.A. Khan, T. Ali, S.S. Dragomir, M.Z. Sarikaya, Hermite-Hadamard type inequalities for conformable fractional integrals. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 112(4), 1033–1048

    Google Scholar 

  11. L. Leindler, Generalization of inequalities of Hardy and Littlewood. Acta Sci. Math. 31, 297–285 (1970)

    MathSciNet  MATH  Google Scholar 

  12. L. Leindler, Further sharpening of inequalities of Hardy and Littlewood. Acta Sci. Math. 54, 285–289 (1990)

    MathSciNet  MATH  Google Scholar 

  13. L. Leindler, Some inequalities pertaining to Bennett’s results. Acta Sci. Math. 58, 261–279 (1993)

    MathSciNet  MATH  Google Scholar 

  14. M.Z. Sarikaya, H. Budak, Opial type inequalities for conformable fractional integrals. RGMIA Res. Rep. Collection 19, 93, 11pp. (2016)

    Google Scholar 

  15. M.Z. Sarikaya, H. Budak, New inequalities of Opial type for conformable fractional integrals. Turkish J. Math. 41(5), 1164–1173 (2017)

    Article  MathSciNet  Google Scholar 

  16. M.Z. Sarikaya, H. Yaldiz, H. Budak, Steffensen’s integral inequality for conformable fractional integrals. Int. J. Anal. Appl. 15(1), 23–30 (2017)

    MATH  Google Scholar 

  17. E. Set, A. Gözpınar, A. Ekinci, Hermite- Hadamard type inequalities via conformable fractional integrals. Acta Math. Univ. Comenian 86(2), 309–320 (2017)

    MathSciNet  MATH  Google Scholar 

  18. C. Yildiz, M.E. Ozdemir, H.K. Onelan, Fractional integral inequalities for different functions. New Trends Math. Sci. 3, 110–117 (2015)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Samir Atwa Saker, Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

    S. H. Saker

  2. Mohammed Ragab Zakie Kenawy, Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt

    M. R. Kenawy

  3. Dumitru Baleanu, Department of Mathematics and Computer Science, Cankaya University, Ankara, Turkey

    D. Baleanu

Authors
  1. S. H. Saker
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  2. M. R. Kenawy
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  3. D. Baleanu
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Corresponding author

Correspondence to S. H. Saker .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  2. Pedagogical Department E. E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece

    John Michael Rassias

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Saker, S.H., Kenawy, M.R., Baleanu, D. (2019). Hardy’s Type Inequalities via Conformable Calculus. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_25

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