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Bounds of Riemann-Liouville Fractional Integrals in General Form via Convex Functions and Their Applications

Author

Listed:
  • Ghulam Farid

    (COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan)

  • Waqas Nazeer

    (Division of Science and Technology, University of Education, Lahore 54000, Pakistan)

  • Muhammad Shoaib Saleem

    (Department of Mathematics, University of Okara, Okara 56300, Pakistan)

  • Sajid Mehmood

    (GBPS Sherani, Hazro Attock 43440, Pakistan)

  • Shin Min Kang

    (Department of Mathematics and RINS, Gyeongsang National University, Jinju 52828, Korea
    Center for General Education, China Medical University, Taiwan, Taichung 40402, Taiwan)

Abstract

In this article, we establish bounds of sum of the left and right sided Riemann Liouville (RL) fractional integrals and related inequalities in general form. A new and novel approach is followed to obtain these results for general Riemann Liouville (RL) fractional integrals. Monotonicity and convexity of functions are used with some usual and straight forward inequalities. The presented results are also have connection with some known and already published results. Applications and motivations of presented results are briefly discussed.

Suggested Citation

  • Ghulam Farid & Waqas Nazeer & Muhammad Shoaib Saleem & Sajid Mehmood & Shin Min Kang, 2018. "Bounds of Riemann-Liouville Fractional Integrals in General Form via Convex Functions and Their Applications," Mathematics, MDPI, vol. 6(11), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:248-:d:182125
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