Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives

Details Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives

2010-07-17

arxiv.org/abs/1007.2937v1

Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), no. 3, 1490--1500

Mathematics

Optimization and Control

Submitted 6/March/2010 to Communications in Nonlinear Science and Numerical Simulation; revised 12/July/2010; accepted for pub

Scientific paper

10.1016/j.cnsns.2010.07.016

We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given. An Euler-Lagrange equation for functionals where the lower and upper bounds of the integral are distinct of the bounds of the Caputo derivative is also proved. Then, the fractional isoperimetric problem is formulated with an integral constraint also containing Caputo derivatives. Normal and abnormal extremals are considered.

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