Discrete Direct Methods in the Fractional Calculus of Variations
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends only on the left Riemann-Liouville fractional derivative. Using Grünwald-Letnikov de.nition, we approximate the objective functional in an equispaced grid as a multi-variable function of the values of the unknown function on mesh points. The problem is then transformed to an ordinary static optimization problem. The solution to the latter problem gives an approximation to the original fractional problem on mesh points.
Fractional calculus fractional calculus of variations direct methods.
Shakoor Pooseh Ricardo Almeida Del m F. M. Torres
Center for Research and Development in Mathematics andApplications, Department of Mathematics, Unive Center for Research and Development in Mathematics and Applications, Department of Mathematics, Univ
国际会议
The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)
南京
英文
1-6
2012-05-14（万方平台首次上网日期，不代表论文的发表时间）