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 via generalized fractional integrals are proved. We also
show that the main results reduce some midpoint inequalities given in
earlier works for Riemann integrals and Riemann-Liouville fractional
integrals. Finally, some new inequalities for $k$-Riemann-Liouville
fractional integrals are presented as special cases of our results.