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Volume 8
Issue 4
10.3390/math8040504
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Article

Certain Hadamard Proportional Fractional Integral Inequalities

by
Gauhar Rahman
1,
Kottakkaran Sooppy Nisar
2,* and
Thabet Abdeljawad
3,4,5,*
1
Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Upper Dir 18000, Pakistan
2
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
3
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
4
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
5
Department of Computer Science and Information Engineering, Asia University, Taichung 40402, Taiwan
*
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(4), 504; https://doi.org/10.3390/math8040504
Submission received: 4 March 2020 / Revised: 27 March 2020 / Accepted: 29 March 2020 / Published: 2 April 2020
(This article belongs to the Special Issue Fractional Differential Equations, Inclusions and Inequalities with Applications)
Versions Notes

Abstract

In this present paper we study the non-local Hadmard proportional integrals recently proposed by Rahman et al. (Advances in Difference Equations, (2019) 2019:454) which containing exponential functions in their kernels. Then we establish certain new weighted fractional integral inequalities involving a family of n ( n ∈ N ) positive functions by utilizing Hadamard proportional fractional integral operator. The inequalities presented in this paper are more general than the inequalities existing in the literature.
Keywords: fractional integrals; hadamard proportional fractional integrals; fractional integral inequalities fractional integrals; hadamard proportional fractional integrals; fractional integral inequalities

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MDPI and ACS Style

Rahman, G.; Sooppy Nisar, K.; Abdeljawad, T. Certain Hadamard Proportional Fractional Integral Inequalities. Mathematics 2020, 8, 504. https://doi.org/10.3390/math8040504

AMA Style

Rahman G, Sooppy Nisar K, Abdeljawad T. Certain Hadamard Proportional Fractional Integral Inequalities. Mathematics. 2020; 8(4):504. https://doi.org/10.3390/math8040504

Chicago/Turabian Style

Rahman, Gauhar, Kottakkaran Sooppy Nisar, and Thabet Abdeljawad. 2020. "Certain Hadamard Proportional Fractional Integral Inequalities" Mathematics 8, no. 4: 504. https://doi.org/10.3390/math8040504

APA Style

Rahman, G., Sooppy Nisar, K., & Abdeljawad, T. (2020). Certain Hadamard Proportional Fractional Integral Inequalities. Mathematics, 8(4), 504. https://doi.org/10.3390/math8040504

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