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Generalized variational problems and Birkhoff equations

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Abstract

In this paper, we present a generalized fractional Birkhoffian equations in terms of Agrawal’s new operators. By choosing different parameter set, we may obtain six kinds of Birkhoffian equations in terms of Riemann–Liouville, Caputo, Riesz and Riesz–Caputo fractional derivatives, respectively. The previous results can be obtained as a special case.

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Acknowledgments

We express our sincere thinks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 10872037, 11742063 and the Natural Science Foundation of Anhui Province under Grant No. 070416226.

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  1. Department of Physics, Anhui Chaohu University, Chaohu, 238000, People’s Republic of China

    Hong-Bin Zhang & Hai-Bo Chen

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  1. Hong-Bin Zhang
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  2. Hai-Bo Chen
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Correspondence to Hong-Bin Zhang.

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Zhang, HB., Chen, HB. Generalized variational problems and Birkhoff equations. Nonlinear Dyn 83, 347–354 (2016). https://doi.org/10.1007/s11071-015-2331-7

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