Discrete-time fractional variational problems

作者：Bastos Nuno R O; Ferreira Rui A C; Torres Delfim F M^*

来源：Signal Processing, 2011, 91(3): 513-524.

DOI：10.1016/j.sigpro.2010.05.001

• Fractional difference calculus
• Calculus of variations
• Fractional summation by parts
• Euler-Lagrange equation
• Natural boundary conditions
• Legendre necessary condition
• Time scale hZ

We introduce a discrete-time fractional calculus of variations on the time scale (hZ)(a), a is an element of R,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 the discrete-derivatives are integer values, and that they converge to the fractional continuous-time solutions when h tends to zero. Our Legendre type condition is useful to eliminate false candidates identified via the Euler-Lagrange fractional equation.

• 出版日期2011-3