Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications

Mathematics

Thabet Abdeljawad¹  Saima Rashid²  MuhammadAslam Noor²  Fahd Jarad³ 

[1] Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia;Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan;Department of Mathematics, Çankaya University, Etimesgut, 06790 Ankara, Turkey;

关键词: convex function;    exponentially convex function;    fractional integrals;    generalized Riemann-liouville fractional integrals;   

DOI  :  10.3390/math7090807

来源: DOAJ

【 摘 要 】

In the present paper, we investigate some Hermite-Hadamard $\left(\mathcal{HH}\right)$ inequalities related to generalized Riemann-Liouville fractional integral $\left(\mathcal{GRLFI}\right)$ via exponentially convex functions. We also show the fundamental identity for $\mathcal{GRLFI}$ having the first order derivative of a given exponentially convex function. Monotonicity and exponentially convexity of functions are used with some traditional and forthright inequalities. In the application part, we give examples and new inequalities for the special means.

【 授权许可】

Unknown