Can we use nonuniform time steps to compute Caputo Fractional derivative in Heat equation FF++ code? (My code is runing but not good result comes)

General Discussion
1

Dear all, i want to know that can we use nonuniform time steps in FreeFem++ to compute the following Caputo derivative for the fractional dervative in FreeFem++ ??

Caputo_Frac
Caputo_Frac1064×385 37 KB

What will its Codes format??.

I have tried like the following way but not good results comes after initial time. I have implemented the nonuniform time step in Heat equation code. Code is running fine but results is not coming good.

Here, is my code:
Heat_nonuniform_timestep.edp (3.2 KB)

Thanks in advance!.