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Open AccessArticle

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

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Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal 18000, Upper Dir, Pakistan
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Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia
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Department of Medical Research, China Medical University, Taichung 40402, Taiwan
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Department of Computer Science and Information Engineering, Asia University, Taichung 40402, Taiwan
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Department of Mathematics, Çankaya University, Etimesgut, Ankara 06790, Turkey
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Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawser 11991, Saudi Arabia
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Authors to whom correspondence should be addressed.
Mathematics 2020, 8(1), 113; https://doi.org/10.3390/math8010113
Received: 14 December 2019 / Revised: 7 January 2020 / Accepted: 7 January 2020 / Published: 11 January 2020
(This article belongs to the Special Issue Special Functions and Applications)
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. View Full-Text
Keywords: fractional integrals; generalized proportional fractional integrals; inequalities; convex functions; bounds fractional integrals; generalized proportional fractional integrals; inequalities; convex functions; bounds
MDPI and ACS Style

Rahman, G.; Abdeljawad, T.; Jarad, F.; Nisar, K.S. Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications. Mathematics 2020, 8, 113.

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