NECESSARY OPTIMALITY CONDITIONS FOR FRACTIONAL DIFFERENCE PROBLEMS OF THE CALCULUS OF VARIATIONS

By Nuno R. O. Bastos, Rui A. C. Ferreira, Delfim F. M. Torres. 2010

136 citations recorded by the source corpus.

We introduce a discrete-time fractional calculus of variations. 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 the solutions of the fractional problems coincide with the solutions of the corresponding non-fractional variational problems when the order of the discrete derivatives is an integer value.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/5d65e2161d7cf0e26ab283d2e40591b143f6f56d

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In Applied Mathematics

In Computational Theory and Mathematics

In Modeling and Simulation

Citations in the corpus

A discrete fractional Gronwall inequality (2012, background): “directions: existence and uniqueness of solutions to discrete fractional equations [4, 5, 7, 12], modelling tumor growths [6], continuity of solutions with respect to initial conditions and also to the order α of the derivative [11], the Euler–Lagrange equation and Legendre’s optimality condition fo”
ON POSITIVE SOLUTIONS TO NONLOCAL FRACTIONAL AND INTEGER-ORDER DIFFERENCE EQUATIONS (2011, background): “[8, 10] and Anastassiou [2, 3] have provided some initial extensions of the discrete fractional calculus to more general time scales.”
FRACTIONAL h-DIFFERENCE EQUATIONS ARISING FROM THE CALCULUS OF VARIATIONS (2011, methodology): “Instead, some examples are solved numerically [8, 9].”
Existence and uniqueness of solution to some discrete fractional boundary value problems of order less than one (2013, background): “It took almost 20 years for researchers to start developing this theory [2,3] but now authors are expanding this field of science in various directions [6,8,14,15].”
The -Transform Method and Delta Type Fractional Difference Operators (2015, background): “Another concept of the fractional sum/difference was introduced in [20–22].”