Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function

• Main Authors: Shu-Bo Chen, Saima Rashid, Zakia Hammouch, Muhammad Aslam Noor, Rehana Ashraf, Yu-Ming Chu
• Format: Article
• Language: English
• Published: SpringerOpen 2020-11-01
• Series: Advances in Difference Equations
• Subjects: Grüss inequality; Young inequality; Generalized fractional integral operator; Raina function
• Online Access: http://link.springer.com/article/10.1186/s13662-020-03108-8

Abstract We establish certain new fractional integral inequalities involving the Raina function for monotonicity of functions that are used with some traditional and forthright inequalities. Taking into consideration the generalized fractional integral with respect to a monotone function, we derive the Grüss and certain other associated variants by using well-known integral inequalities such as Young, Lah–Ribarič, and Jensen integral inequalities. In the concluding section, we present several special cases of fractional integral inequalities involving generalized Riemann–Liouville, k-fractional, Hadamard fractional, Katugampola fractional, ( k , s ) $(k,s)$ -fractional, and Riemann–Liouville-type fractional integral operators. Moreover, we also propose their pertinence with other related known outcomes.