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# Fractional Calculus 分数阶微积分

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## 1. Input Fractional Calculus into Calculator

Input sin(0.5,x) for the 0.5th order derivative of sin(x), which is denoted by sin^((0.5))(x). It is differrent from power of sin(x) as sin(x)^2. sin(0.5,x) can be computed and plot. d(sin(x),x,0.5) computes the 0.5th order derivative of sin(x). If you want to hold it (not evaluate), use the derivative holder ds(y,x,0.5).

## 3. Difference between Caputo definition and the Riemann-Liouville definition

The Davison-Essex (Caputo) and the Riemann-Liouville definitions are different in the following aspect: in the D-E formula, differentiation is performed first, then integration; in the R-L formula it is the other way around. The D-E definition implemented, thus, maps constants to zero, imitating integer order differentiation, while the R-L definition does not. This property of the D-E definition makes it suitable to work with initial value problems for fractional differential equations. So the Caputo definition is used here. ﻿