On the existence and uniqueness of solutions of a class of fractional differential equations

In this paper, we investigate the existence and uniqueness of solutions for the following class of multiorder fractional differential equations D γ1,δ1 β1 ···D γn,δn βn u(t) := n i=1 D γi ,δi βi u(t) := D γi ,δi βi ,n u(t) = f t,u(t) , t∈ [0, 1], u(0) = 0, n i=1 δi 1, γi > 0, βi > 0, 1 i n, where D γi ,δi βi ,n denotes the generalized Erdélyi–Kober operator of fractional derivative of order δi . Moreover, some properties concerning the positive, maximal, minimal, and continuation of solutions are obtained. © 2006 Elsevier Inc. All rights reserved.