Fractal dimension of Katugampola fractional integral of continuous functions with unbounded variation

The present paper mainly explore fractal dimension of Katugampola fractional integral of continuous functions with unbounded variation. We prove that Box dimension and Hausdorff dimension of Katugampola fractional integral of continuous functions with finite unbounded variation points are 1. Furthermore, we get an important conclusion that Box dimension and Hausdorff dimension of Katugampola fractional integral of continuous functions with infinite and countable unbounded variation points are 1.