New aspects of Opial-type integral inequalities

Abstract

Abstract In this manuscript, we prove new aspects for several Opial-type integral inequalities for the left and right Caputo–Fabrizio operators with nonsingular kernel. For this purpose we use the inequalities obtained by Andrić et al. (Integral Transforms Spec. Funct. 25(4):324–335, 2014), which is the generalization of an inequality of Agarwal and Pang (Opial Inequalities with Applications in Differential and Difference Equations, 1995). Besides, examples are presented to validate the reported results.

Keywords

• Opial-type inequality
• The left operator
• The right operator
• The left integral
• The right integral
• Caputo–Fabrizio fractional derivative