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

• Main Authors: Saima Rashid, Thabet Abdeljawad, Fahd Jarad, Muhammad Aslam Noor
• Format: Article
• Language: English
• Published: MDPI AG 2019-09-01
• Series: Mathematics
• Subjects: convex function; exponentially convex function; fractional integrals; generalized Riemann-liouville fractional integrals
• Online Access: https://www.mdpi.com/2227-7390/7/9/807

In the present paper, we investigate some Hermite-Hadamard <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi mathvariant="script">HH</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> inequalities related to generalized Riemann-Liouville fractional integral <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi mathvariant="script">GRLFI</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> via exponentially convex functions. We also show the fundamental identity for <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">GRLFI</mi> </semantics> </math> </inline-formula> 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.