The Euler–Lagrange and Legendre equations for functionals involving distributed–order fractional derivatives

摘要

In this paper, we extend some fractional calculus of variations results by considering functionals depending on distributed–order fractional derivatives. Using variational techniques, we deduce optimal necessary conditions of Euler–Lagrange and Legendre type. We also study the case where integral and holonomic constraints are imposed. Finally, a numerical procedure is given to solve some proposed problems.