Fractional Calculus on Time Scales

2012/02/14 by Bastos, Nuno R. O.
#26A33 #26E70 #39A12 #49K05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1202.2960

Abstract

We introduce a discrete-time fractional calculus of variations on the time scales ℤ and (hℤ)_a. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. We also give new definitions of fractional derivatives and integrals on time scales via the inverse generalized Laplace transform.

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