2016/01/01 by Michèle Caputo, Mauro Fabrizio · 538 citations
Engineering · Mathematics · #Applied mathematics #Composite Structure Analysis and Optimization #Exponential function #Fractional Differential Equations Solutions #Mathematical analysis #Mathematics #Thermoelastic and Magnetoelastic Phenomena
paper · doi:10.18576/pfda/020101
published in Progress in Fractional Differentiation and Applications 2(1), 1-11
openalex publication_date 2016/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 mode ls 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.