It is very happy to share that FractionalCalculus.jl is now supporting symbolic fractional differentiation and integration!!!
With the help of SymbolicUtils.jl, it is easy to first declare rules and apply defined rules to the expression
julia> using FractionalCalculus, SymbolicUtils
julia> @syms x
All we need to use are semidiff and semiint functions to compute fractional differentiation and integration.
julia> semidiff(log(x))
log(4x) / sqrt(πx)
julia> semiint(x^2)
0.6018022224509401(x^2.5)
Bingo!! Enjoy yourself~