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

China University of Mining; Civil Engineering; Deep Underground Engineering; Department of Electrical Engineering); J. A. Tenreiro Machado (Institute of Engineering; Polytechnic of Porto; State Key Laboratory for Geomechanics; Technology; Technology); Xiao-Jun Yang (School of Mechanics

arxiv: 1611.09200 · v1 · pith:7OHT4KXFnew · submitted 2016-11-21 · ❄️ cond-mat.stat-mech

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

Xiao-Jun Yang (School of Mechanics , Civil Engineering , China University of Mining , Technology , State Key Laboratory for Geomechanics , Deep Underground Engineering , Technology) , J. A. Tenreiro Machado (Institute of Engineering

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Polytechnic of Porto Department of Electrical Engineering)

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classification ❄️ cond-mat.stat-mech

keywords ordervariableanomalousdiffusionfractionaloperatoranalyzedapplication

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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.

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

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