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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Several Fractional Differences and Their Applications to Discrete Maps

Journal of Applied Nonlinear Dynamics 4(4) (2015) 339--348 | DOI:10.5890/JAND.2015.11.001

Guo-Cheng Wu$^{1}$, Dumitru Baleanu$^{2}$,$^{3}$, Sheng-Da Zeng$^{3}$

$^{1}$ Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang 641100, China

$^{2}$ Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06530, Balgat, Ankara, Turkey

$^{3}$ Institute of Space Sciences, Magurele-Bucharest, Romania

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Abstract

Several definitions of fractional differences are discussed. Their applications to fractional maps are compared. As an example, the logistic equation of integer order is discretized by these fractional difference methods. The comparative results show that the discrete fractional calculus is an efficient tool and the maps derived in this way have simpler forms but hold rich dynamical behaviors.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (Grant No.11301257), the Innovative Team Program of Sichuan Provincial Universities (Grant No. 13TD0001) and the Seed Funds for Major Science and Technology Innovation Projects of Sichuan Provincial Education Department (Grant No.14CZ0026).

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