Hamilton’s principle with variable order fractional derivatives

Abstract

Abstract We propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler-Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined through a constitutive equation. Necessary conditions for the existence of the minimizer are obtained. They imply various known results in a special cases.