On simple iterative fractional order differential equations

In this paper, the simple fractional iterative differential equation will be the focus of study D β v ( s ) = v n ( s ) , v ( s 0 ) = a . where s 0, v 0 ∈ I = [0, b], and 0 < β < 1. One class of the iterative fractional differential equations is the simple iterative fractional differential equation. In this paper, the local existence and uniqueness results for the fractional order of degree n of simple iterative fractional differential equation are proven and the solutions found by using power series.