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) + 2 0 φ(α)y(α)(t) dα = 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. © 2006 Elsevier Inc. All rights reserved