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Open AccessArticle

Certain Hadamard Proportional Fractional Integral Inequalities

Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Upper Dir 18000, Pakistan
Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
Department of Computer Science and Information Engineering, Asia University, Taichung 40402, Taiwan
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(4), 504;
Received: 4 March 2020 / Revised: 27 March 2020 / Accepted: 29 March 2020 / Published: 2 April 2020
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. View Full-Text
Keywords: fractional integrals; hadamard proportional fractional integrals; fractional integral inequalities fractional integrals; hadamard proportional fractional integrals; fractional integral inequalities
MDPI and ACS Style

Rahman, G.; Sooppy Nisar, K.; Abdeljawad, T. Certain Hadamard Proportional Fractional Integral Inequalities. Mathematics 2020, 8, 504.

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