Fractional midpoint inequalities for co-ordinated ($ \mathrm{s_1}, {s_2} $)-convex functions: A new perspective

In this study, some Hermite-Hadamard type inequalities are investigated for differentiable co -ordinated( \mathrm{s_1}, {s_2} )-convex functions in the second sense. In particular, generalizations of midpoint-type inequalities are established on rectangular domains in the plane. Additionally, several new inequalities are derived for the cases of Riemann-Liouville and k-Riemann-Liouville fractional integrals by considering special cases of the main results.