Abstract

In this paper, we present two new ``transfer formulas'' for some generalized fractional derivative operators, and derive a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and generalized fractional derivative operator. As a result, we obtain constants of motion that are valid along Euler-Lagrange extremals for mixed classical and fractional derivatives. This theorem provides an explicit algorithmic way to compute constants of motion for Lagrangian systems with classical and generalized fractional derivative operator admitting a symmetry. Results from previous literature can be obtained as a special case of one.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 2
Year: 2017

DOI: 10.12732/ijam.v30i2.5

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