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Applications of New Time and Spatial Fractional Derivatives with Exponential Kernels |
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PP: 1-11 |
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doi:10.18576/pfda/020101
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Author(s) |
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Michele Caputo,
Mauro Fabrizio,
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Abstract |
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| In the paper, we present some applications and features related with the new notions of fractional derivatives with a time
exponential kernel and with spatial Gauss kernel for gradient and Laplacian operators. Specifically, for these new models we have
proved the coherence with the thermodynamic laws. Hence, we have revised the standard linear solid of Zener within continuum
mechanics and the model of Cole and Cole inside electromagnetism by these new fractional operators. Moreover, by the Gaussian
fractional gradient and through numerical simulations, we have studied the bell shaped filtering effects comparing the results with
exponential and Caputo kernel. |
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