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Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications

Author

Listed:
  • Gauhar Rahman

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

  • Thabet Abdeljawad

    (Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
    Department of Medical Research, China Medical University, Taichung 40402, Taiwan
    Department of Computer Science and Information Engineering, Asia University, Taichung 40402, Taiwan)

  • Fahd Jarad

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

  • Kottakkaran Sooppy Nisar

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

Abstract

In this paper, our objective is to apply a new approach to establish bounds of sums of left and right proportional fractional integrals of a general type and obtain some related inequalities. From the obtained results, we deduce some new inequalities for classical generalized proportional fractional integrals as corollaries. These inequalities have a connection with some known and existing inequalities which are mentioned in the literature. In addition, some applications of the main results are presented.

Suggested Citation

  • Gauhar Rahman & Thabet Abdeljawad & Fahd Jarad & Kottakkaran Sooppy Nisar, 2020. "Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications," Mathematics, MDPI, vol. 8(1), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:113-:d:307698
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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.
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