there are 3 way to input derivative y: y', y(1,x), or ds(y,x,1)
there are 3 way to input second order derivative y: y'', y(2,x), or ds(y,x,2)
Input y(1,x) as first order differential equation `dy/dx - 2y=0`
Integral equation is extend to fractional integral equation by minus fractional order.
e.g. input ds(y,x, -0.5) as semi integral equation `d^-0.5/dx^-0.5 y = 2y`
4. Solve (fractional) differential equation
Method to solve fractional differential equation is similar to differential equation.
Integral equation can be converted to differential equation by differentiating both sides. Some fractional integral equation aslo can be
converted to fractional differential equation, but not every fractional integral equation can be converted.
All of their solutions are in the same format exp(k x). When the a order of the differential equation decreased from 2 to 0.5, its solution increased from exp(sqrt(2)*x) to exp(4x).
When the a order of the differential equation decreased from -0.5 to -1, its solution increased from exp(1/4 x) to exp(1/2 x).
Their change are similar to a change of the a order in fractional derivative `d^a/dx^a x` in below picture.