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A new fractional operator of variable order: Application in the description of anomalous diffusion

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  • Yang, Xiao-Jun
  • Machado, J.A. Tenreiro

Abstract

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.

Suggested Citation

  • Yang, Xiao-Jun & Machado, J.A. Tenreiro, 2017. "A new fractional operator of variable order: Application in the description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 276-283.
    • Handle: RePEc:eee:phsmap:v:481:y:2017:i:c:p:276-283
    DOI: 10.1016/j.physa.2017.04.054
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    References listed on IDEAS

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    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
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