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

الملخص EN

The paper researches the continuity of fractal interpolation function’s fractional order integral on [0,+∞) and judges whether fractional order integral of fractal interpolation function is still a fractal interpolation function on [0,b](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,+∞) and fractional order integral of fractal interpolation is still a fractal interpolation function on the interval [0,b].