init

FOTF Toolbox/riemannsym.m

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+function dy=riemannsym(f,alpha,t0,t)
+% riemannsym Symbolic computing of Roemann-Liouville derivatives
+
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 18 May, 2022 
+   arguments, f(1,1), alpha(1,1), t0(1,1)=0, t(1,1)=symvar(f), end
+   syms tau; alpha=sym(alpha); 
+   switch class(f)
+      case 'sym', F=subs(f,t,tau);
+      case 'symfun', F=f(tau);
+      otherwise, error('f must be a symbolic expression')
+   end
+   if alpha<0, alpha=-alpha;
+      dy=1/gamma(alpha)*int(F/(t-tau)^(1-alpha),tau,t0,t);
+   elseif alpha==0, dy=f;
+   else, n=ceil(alpha);
+      f1=int(F/(t-tau)^(1+alpha-n),tau,t0,t);
+      dy=diff(f1,t,n)/gamma(n-alpha);
+   end
+end