Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach

Abstract In this paper, we first establish a novel integral identity involving functions of two variables by using the Riemann–Liouville fractional integrals. By taking the modulus of this newly derived identity, we obtain a new form of Newton-type inequality specifically for differentiable co-ordinated convex functions. Moreover, we give example using graph in order to show that our main results are correct. In addition, we derive several new inequalities by employing Hölder’s inequality. Furthermore, we present previously achieved results and new results by using special cases of the obtained theorems. These results not only extend existing inequalities in the literature but also offer new insights into the interplay between fractional calculus and convex analysis.