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Tempered Fractional Integral Inequalities for Convex Functions

Author

Listed:
  • Gauhar Rahman

    (Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Upper Dir 18000, Pakistan)

  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia)

  • Thabet Abdeljawad

    (Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, KSA, Saudi Arabia
    Department of Medical Research, China Medical University, Taichung 40402, Taiwan
    Department of Computer Science and Information Engineering, Asia University, Taichung 40402, Taiwan)

Abstract

Certain new inequalities for convex functions by utilizing the tempered fractional integral are established in this paper. We also established some new results by employing the connections between the tempered fractional integral with the (R-L) fractional integral. Several special cases of the main result are also presented. The obtained results are more in a general form as it reduced certain existing results of Dahmani (2012) and Liu et al. (2009) by employing some particular values of the parameters.

Suggested Citation

  • Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad, 2020. "Tempered Fractional Integral Inequalities for Convex Functions," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:500-:d:340453
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    References listed on IDEAS

    as
    1. J. A. Tenreiro Machado & Alexandra M. S. F. Galhano & Juan J. Trujillo, 2014. "On development of fractional calculus during the last fifty years," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 577-582, January.
    2. Gauhar Rahman & Zafar Ullah & Aftab Khan & Erhan Set & Kottakkaran Sooppy Nisar, 2019. "Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators," Mathematics, MDPI, vol. 7(4), pages 1-9, April.
    3. Set, Erhan & Tomar, Muharrem & Sarikaya, Mehmet Zeki, 2015. "On generalized Grüss type inequalities for k-fractional integrals," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 29-34.
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