  The existence of solutions to Cauchy type problems of linear
Riemann-Liouville fractional differential equations with variable coefficients
is considered in a space of integrable functions. First, we consider the
existence and uniqueness of solution for a Cauchy type problem with special
initial conditions in the space of integrable functions. Then we provide an
example of the problem that has no solution in the space of integrable
functions. We give a solving method and a representation of solutions for the
Cauchy type problem. Last we give some examples.
