Fractal dimension of Katugampola fractional integral of vector-valued functions

Calculating fractal dimension of the graph a function not simple even for real-valued functions. While through this paper, our intention is to provide some initial theories graphs vector-valued In particular, we give fresh attempt estimate Katugampola fractional integral continuous bounded variation defined on closed interval in $$\mathbb {R}.$$ We prove that 1 and so its integral. Further, Hölder function, an upper bound box each coordinate function.