Fractional calculus of fractal interpolation function on \([0,b]\) (\(b>0\)) (Q1724638)

Summary: The paper researches the continuity of fractal interpolation function's fractional order integral on \([0,+\infty)\) 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 \([0,+\infty)\) and fractional order integral of fractal interpolation is still a fractal interpolation function on the interval \([0,b]\).