ODE system solution with Mathematica or MATLAB

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I need solution of this system with Mathematica or MATLAB:

$\frac{\partial f(i,j,t)}{\partial t}=\sum_{i_{0}<i}^{}\sum_{j_{0}}^{}a(i,j)b(i,j,i_{0},j_{0})f(i_{0},j_{0},t)-a(i,j)f(i,j,t)$

Can you help me?

Thank you.