# Question:How to calculate the fractional derivative of an expression manually

## Question:How to calculate the fractional derivative of an expression manually

Maple 2022

Dear All,

I have a question about "fraddiff" command to compute the fractional derivative of a function.
I need to produce  a procedure to manually compute Caputo fractional derivative of a function, instead of using "fracdiff", as the following:

Frac_C:=proc()
description "Frac_C(function,lower bound, variable (upper bound), order of differentiation)";
a:=args[2];
x:=args[3];
alpha:=args[4];
f:=unapply(args[1],args[3]);
m:=ceil(alpha);
return 1/GAMMA(m-alpha)*int((x-tau)^(m-alpha-1)*diff(f(tau),tau\$m),tau=a..x);
end proc;

when I call the above procedure, as Frac_C(x^(3.4),0,x,3/4), Maple is not able to calculate the integral defined in the Caputo fractional derivative. However, I saw the pre-defined Maple command, namely fracdiff, is able to do.
Where is the trouble?
can anyone help me?

It is worth mentioning that I can calculate the fractional derivative of a functional by procedure "Frac_C()" when I try to use it at the given x as the following which is not desirable for me.
evalf(subs(x=2,Frac_C(x^(3.4),0,x,3/4)));
evalf(subs(x=2,fracdiff(x^(3.4),x,3/4)));

Best wishes

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