  Fractional derivatives are generalization to classical integer-order
derivatives. The rules which are true for classical derivative need not hold
for the fractional derivatives, for example, we cannot simply add the
fractional orders $\alpha$ and $\beta$ in ${}_0^{C}\mathrm{D}_t^\alpha
{}_0^{C}\mathrm{D}_t^\beta$ to produce the fractional derivative
${}_0^{C}\mathrm{D}_t^{\alpha+\beta}$ of order $\alpha+\beta$, in general. In
this article we discuss the details of such compositions and propose the
conditions to split a linear fractional differential equation into the systems
involving lower order derivatives. Further, we provide some examples, which
show that the related results in the literature are sufficient but not
necessary conditions.
