init

FOTF Toolbox/caputosym.m

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+function dy=caputosym(f,alpha,t0,t)
+%caputosym evaluates symbolically Caputo derivatives
+%
+%    dy=caputosym(f,alpha,t0,t)
+%
+%    f - symbolic expression or symbolic function 
+%    alpha - fractional order, must be a symbolic number
+%    t0 - initial time, default of 0
+%    t - final time, woth default of symbolic t
+
+% 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
+   if alpha<=0, dy=riemannsym(f,alpha,t0,t); return; end
+   syms tau; alpha=sym(alpha); m=ceil(alpha); gam=m-alpha;
+   switch class(f)
+      case 'sym', F=diff(subs(f,t,tau),m);
+      case 'symfun', F=diff(f(tau),m);
+      otherwise, error('f must be a symbolic expression')
+   end
+   dy=1/gamma(gam)*int(F/(t-tau)^(1-gam),tau,t0,t);
+end