THE PROPERTIES OF FRACTIONAL ORDER CALCULUS OF FRACTAL INTERPOLATION FUNCTION OF BROKEN LINE SEGMENTS

In order to research the properties of the fractional order calculus of broken line segments' fractal interpolation function (FIF) generated by the linear iterated function system (IFS), the concepts of the Riemann-Liouville fractional order calculus and the method of the IFS are used to prove the properties of the fractional calculus of the broken line segments' FIF generated by the linear IFS. There are two conclusions as follows. First, the fractional order integral of the broken line segments' FIF formed by the linear IFS is continuous and first-order differentiable on the closed interval 10, x N 1. Second, the broken line segments' FIF formed by the linear IFS exists with fractional order differential, but the differential function is not continuous.