Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition |
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Authors: | Mohammad Khorrami Ahmad Shariati Amir Aghamohammadi Amir H Fatollahi |
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Institution: | Department of Physics, Alzahra University, Tehran 19938-93973, Iran |
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Abstract: | It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time. |
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Keywords: | Diffusion equation Anomalous diffusion Fractional derivative |
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