CALCULUS OF VARIATIONS ON TIME SCALES

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NECESSARY OPTIMALITY CONDITIONS FOR FRACTIONAL DIFFERENCE PROBLEMS OF THE CALCULUS OF VARIATIONS (2010, background): “22) and (23) are the fractional discrete-time natural boundary conditions. The next result is a particular case of our Theorem 3.5. Corollary 1 (The discrete-time Euler–Lagrange equation – cf., e.g., [12, 14]). If y˜ is a solution to the problem L(y(·)) = bX−1 t=a L(t,y(t +1),∆y(t)) −→ min y(a) = A,”
Higher-Order Calculus of Variations on Time Scales (2007, background): “tain the Euler-Lagrange necessary optimality condition for problem (P) as soon as we know how to do it for (1), this is not the case on the time scale setting. The Euler-Lagrange equation obtained in [2, 4] for (1) follow the classical proof, substituting the usual integration by parts formula by in”
FRACTIONAL h-DIFFERENCE EQUATIONS ARISING FROM THE CALCULUS OF VARIATIONS (2011, unknown): “, in [12, 20].”
An application of time scales to economics (2006, methodology): “Many nice properties and examples of the nabla exponential function can be found in the book by Martin Bohner and Allan Peterson [13, Chapter 3].”
Calculus of variations on time scales with nabla derivatives (2008, background): “The main result of [4] is an Euler-Lagrange ecessary optimality equation for a first order variational problem involving delta derivativ es on a time scale T: Theorem 1 ([4]).”