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Certain Hadamard Proportional Fractional Integral Inequalities

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, 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

In this present paper we study the non-local Hadmard proportional integrals recently proposed by Rahman et al. (Advances in Difference Equations, (2019) 2019:454) which containing exponential functions in their kernels. Then we establish certain new weighted fractional integral inequalities involving a family of n ( n ∈ N ) positive functions by utilizing Hadamard proportional fractional integral operator. The inequalities presented in this paper are more general than the inequalities existing in the literature.

Suggested Citation

  • Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad, 2020. "Certain Hadamard Proportional Fractional Integral Inequalities," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:504-:d:340493
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    References listed on IDEAS

    as
    1. 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.
    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.
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    Cited by:

    1. Abdellatif Ben Makhlouf & Lassaad Mchiri & Hakeem A. Othman & Hafedh M. S. Rguigui & Salah Boulaaras, 2023. "Proportional Itô–Doob Stochastic Fractional Order Systems," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    2. Osama Moaaz & Ahmed E. Abouelregal & Meshari Alesemi, 2022. "Moore–Gibson–Thompson Photothermal Model with a Proportional Caputo Fractional Derivative for a Rotating Magneto-Thermoelastic Semiconducting Material," Mathematics, MDPI, vol. 10(17), pages 1-21, August.

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