AbstractSome new integral inequalities for strongly $(\alpha ,h-m)$
(
α
,
h
−
m
)
-convex functions via generalized Riemann–Liouville fractional integrals are established. The outcomes of this paper provide refinements of some fractional integral inequalities for strongly convex, strongly m-convex, strongly $(\alpha ,m)$
(
α
,
m
)
-convex, and strongly $(h-m)$
(
h
−
m
)
-convex functions. Also, the refinements of error estimations of these inequalities are obtained by using two fractional integral identities. Moreover, using a parameter substitution and a constant multiplier, k-fractional versions of established inequalities are also given.