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

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.

arXiv comment2 figures, 13 pages

References in corpus (4)

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• From Diffusion to Anomalous Diffusion: A Century after Einstein's Brownian Motion
• A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow
• Approximate Solutions to Fractional Subdiffusion Equations: The heat-balance integral method

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