  We consider the canonical fundamental systems of solutions of linear
homogeneous Caputo fractional differential equations with continuous variable
coefficients. Here we gained a series-representation of the canonical
fundamental system by coefficients of the considered equations and the
representation of solution to initial value problems using the canonical
fundamental system. According to our results, the canonical fundamental system
of solutions to linear homogeneous differential equation with Caputo fractional
derivatives and continuous variable coefficients has different representations
according to the distributions of the lowest order of the fractional
derivatives in the equation and the distance from the highest order to its
adjacent order of the fractional derivatives in the equation.

Classical Analysis and ODEs