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arXiv · 1704.06486

Combined Fractional Variational Problems of Variable Order and Some Computational Aspects

Dina Tavares·Ricardo Almeida·Delfim F. M. Torres
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Abstract

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.

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Dina Tavares, Ricardo Almeida, Delfim F. M. Torres. 2017-04-21. Combined Fractional Variational Problems of Variable Order and Some Computational Aspects. https://doi.org/10.1016/j.cam.2017.04.042

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