Fractional Calculus of Fractal Interpolation Function on [0,b](b>0)

Abstract

The paper researches the continuity of fractal interpolation function’s fractional order integral on $[0,+\infty )\mathrm{}$ and judges whether fractional order integral of fractal interpolation function is still a fractal interpolation function on $\mathrm{[0,b]}\mathrm{(b>0)}$ or not. Relevant theorems of iterated function system and Riemann-Liouville fractional order calculus are used to prove the above researched content. The conclusion indicates that fractional order integral of fractal interpolation function is a continuous function on $[0,+\infty )\mathrm{}$ and fractional order integral of fractal interpolation is still a fractal interpolation function on the interval $\mathrm{[0,b]}$.