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I am trying to solve a fractional-order 2-compartment model using the method of manufactured solution (MMS). I do understand the concept of MMS, but I am not sure how to come with a Mathematica code for such a system enter image description here

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    $\begingroup$ I think that you are missing a source term to be able to apply the method. $\endgroup$
    – nicoguaro
    Jul 10 at 14:20
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Your problem can be rewritten as

$$\mathbf{x}' = A \mathbf{x}\, .$$

Nevertheless, to apply the method of manufactured solutions you need a system of the form

$$\mathbf{x}' = A \mathbf{x} + \mathbf{b}\, ,$$

to use

$$\mathbf{b}_\text{manu} = \mathbf{x}_\text{manu} ' -A \mathbf{x}_\text{manu} \, ,$$

where $\mathbf{x}_\text{manu}$ is the proposed solution.

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