Formulation of Euler–Lagrange equations for fractional variational problems

Variational formulation of problems involving fractional order differential operators

In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). These fractional derivatives lead to non-symmetric boundary value problems, which are investigated from a variational point of view. The variational problem for the Riemann-Liouville case is coercive on the space H α/2 0 (0, 1) but the ...

Variational Formulation of Problems and Variational Methods

A novel variational formulation for thermoelastic problems

Article history: Received 26 March 2014 Received in revised form 25 September 2014 Accepted 27 September 2014 Available online 15 October 2014

Fractional Action-like Variational Problems *

Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations. 2000 Mathematics Subject Classification: 49K10, 49S05.

Discrete-time fractional variational problems

We introduce a discrete-time fractional calculus of variations on the time scale hZ, h > 0. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of ...