Combined Fractional Variational Problems of Variable Order and Some  Computational Aspects

Tavares, Dina; Almeida, Ricardo; Torres, Delfim F. M.

http://hdl.handle.net/10400.8/3309

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Authors

Tavares, Dina

Almeida, Ricardo

Torres, Delfim F. M.

Abstract(s)

We study two generalizations of fractional variational problems by considering higher-order derivatives and a state time delay. We prove a higher-order integration by parts formula involving a Caputo fractional derivative of variable order and we establish several necessary optimality conditions for functionals containing a combined Caputo derivative of variable fractional order. Because the endpoint is considered to be free, we also deduce associated transversality conditions. In the end, we consider functionals with a time delay and deduce corresponding optimality conditions. Some examples are given to illustrate the new results. Computational aspects are discussed using the open source software package Chebfun.