On simple iterative fractional order differential equations - Damag, Faten Hasan Mohammed; Kilicman, Adem (AIP Publishing, 2016)
In this paper, the simple fractional iterative differential equation will be the focus of study Dβv(s)=vn(s), v(s0)=a. where s0, v0 ∈ 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.