Fractional Hermite Interpolation For Non-smooth Functions

The interpolation of functions is the foundation of numerical computations.However,the highly accurate approximation for non-smooth functions is a challenge in science and engineering.This paper is devoted to constructing fractional Hermite interpolation for non-smooth functions,which are based on the local fractional Taylor formulas,and deriving the corresponding explicit expressions and error remainders.Then,we discuss the convergence order of the piecewise hybrid interpolation,which is a combination of fractional Hermite interpolation and traditional Hermite interpolation.Finally,some numerical examples are presented to show the high precision of the fractional Hermite interpolation method.