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

Gauhar Rahman, Thabet Abdeljawad, Fahd Jarad and Kottakkaran Sooppy Nisar
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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
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

Mathematics, 2020, vol. 8, issue 1, 1-19

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.

Keywords: fractional integrals; generalized proportional fractional integrals; inequalities; convex functions; bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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