Abstract
We propose an alternative derivation of the subdiffusion equation with a source term. Basing on this approach, we obtain the variable-order and the distributed-order equations that reduce to the well-known Riemann–Liouville and Caputo forms of the time-fractional subdiffusion equation. We find out that the naive inclusion of sources/sinks as a separate term is correct for the equations with the Riemann–Liouville derivative. However, for the equations with the Caputo derivative, the source term must go under a fractional integral.
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