Fractional order systems: an Approach to the initial value problem and its stability

In this paper, we discuss the initial value problem and its stability for fractional autonomous order systems in the usual sense. Our result in the linear case is equivalent to the one known in literature; this establishes the mathematic technique in order to solve the problem with initial trajectory that will be presented in future studies. The conditions that are shown are simpler to verify than the ones that are commonly known and have a close relationship with the calculations for the integer case.