Estimates of upper bound for differentiable mappings related to Katugampola fractional integrals and $ p $-convex mappings

We use the definition of a fractional integral operators, recently introduced by Katugampola, to establish a parameterized identity associated with differentiable mappings. The identity is then used to derive the estimates of upper bound for mappings whose first derivatives absolute values are $ p $-convex mappings. Four examples are also provided to illustrate the obtained results.