On a nonlinear distributed order fractional differential equation

We study the existence and the uniqueness of mild and classical solutions for a class of equations of the form y((2))(t) + integral(2)(0) phi(alpha)y((alpha))(t)d alpha = f (y, t). Such equations arise in distributed derivatives models of viscoelasticity and system identification theory. We also formulate a variational principle for a more general equation based on a method of doubling of variables for such equations. (c) 2006 Elsevier Inc. All rights reserved.