Abstract
Many scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown in popularity as a result of its capacity to quickly solve real-world problems. First, we establish new fractional inequalities of the Hadamard-Mercer, Pachpatte-Mercer, and Dragomir-Agarwal-Mercer types containing an exponential kernel. In this regard, the inequality proved by Jensen and Mercer plays a major role in our main results. Integral inequalities involving convexity have a wide range of applications in several domains of mathematics where symmetry is important. Both convexity and symmetry are closely linked with each other; when working on one of the topics, you can apply what you have learned to the other. We consider a new identity for differentiable mappings and present its companion bound for the Dragomir-Agarwal-Mercer type inequality employing a convex function. Applications involving matrices are presented. Finally, we conclude our article and discuss its future scope.