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Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications

Author

Listed:
  • Saima Rashid

    (Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan)

  • Thabet Abdeljawad

    (Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia)

  • Fahd Jarad

    (Department of Mathematics, Çankaya University, Etimesgut, 06790 Ankara, Turkey)

  • Muhammad Aslam Noor

    (Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan)

Abstract

In the present paper, we investigate some Hermite-Hadamard ( HH ) inequalities related to generalized Riemann-Liouville fractional integral ( GRLFI ) via exponentially convex functions. We also show the fundamental identity for GRLFI having the first order derivative of a given exponentially convex function. Monotonicity and exponentially convexity of functions are used with some traditional and forthright inequalities. In the application part, we give examples and new inequalities for the special means.

Suggested Citation

  • Saima Rashid & Thabet Abdeljawad & Fahd Jarad & Muhammad Aslam Noor, 2019. "Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications," Mathematics, MDPI, vol. 7(9), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:807-:d:263171
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    References listed on IDEAS

    as
    1. Thabet Abdeljawad & Qasem M. Al-Mdallal & Mohamed A. Hajji, 2017. "Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-8, June.
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    Cited by:

    1. Watcharin Chartbupapan & Ovidiu Bagdasar & Kanit Mukdasai, 2020. "A Novel Delay-Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation," Mathematics, MDPI, vol. 8(1), pages 1-10, January.
    2. Saima Rashid & Muhammad Aslam Noor & Khalida Inayat Noor & Farhat Safdar & Yu-Ming Chu, 2019. "Hermite-Hadamard Type Inequalities for the Class of Convex Functions on Time Scale," Mathematics, MDPI, vol. 7(10), pages 1-20, October.

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