Generalized fractional midpoint type inequalities for co-ordinated convex functions

Abstract

In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities viageneralized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemannintegrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for $k$-Riemann-Liouville fractional integrals are presented as special cases of our results.