18 research outputs found
Fractional Euler-Lagrange differential equations via Caputo derivatives
We review some recent results of the fractional variational calculus.
Necessary optimality conditions of Euler-Lagrange type for functionals with a
Lagrangian containing left and right Caputo derivatives are given. Several
problems are considered: with fixed or free boundary conditions, and in
presence of integral constraints that also depend on Caputo derivatives.Comment: This is a preprint of a paper whose final and definite form will
appear as Chapter 9 of the book Fractional Dynamics and Control, D. Baleanu
et al. (eds.), Springer New York, 2012, DOI:10.1007/978-1-4614-0457-6_9, in
pres
Variational Problems Involving a Caputo-Type Fractional Derivative
We study calculus of variations problems, where the Lagrange function depends on the
Caputo-Katugampola fractional derivative. This type of fractional operator is a generalization
of the Caputo and the Caputo–Hadamard fractional derivatives, with dependence on a real
parameter ρ. We present sufficient and necessary conditions of first and second order to
determine the extremizers of a functional. The cases of integral and holomonic constraints are also considered
Wave equation for generalized Zener model containing complex order fractional derivatives
A non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete
A non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete
Approximate solutions of time and time-space fractional wave equations with variable coefficients
Fractional thermoelasticity problem for an infinite solid with a penny-shaped crack under prescribed heat flux across its surfaces
Some orthogonal polynomials on the finite interval and Gaussian quadrature rules for fractional Riemann‐Liouville integrals
A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems
We develop a simple and accurate method to solve fractional variational and fractional optimal control problems with dependence on Caputo and Riemann–Liouville operators. Using known formulas for computing fractional derivatives of polynomials, we rewrite the fractional functional dynamical optimization problem as a classical static optimization problem. The method for classical optimal control problems is called Ritz’s method. Examples show that the proposed approach is more accurate than recent methods available in the literature. © 2016, Springer Science+Business Media New York