The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Applications of New Time and Spatial Fractional Derivatives with Exponential Kernels
Abstract
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.
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Citations
Cites
Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics
Cole, K. S., & Cole, R. H. (1941) · The Journal of Chemical Physics · doi:10.1063/1.1750906 · Cited by 10,152
Cited by
Atangana, A., & Gómez-Aguilar, J. F. (2018) · The European Physical Journal Plus · doi:10.1140/epjp/i2018-12021-3 · Cited by 425
Metadata
- Authors
- Caputo, M., & Fabrizio, M.
- Venue
- Progress in Fractional Differentiation and Applications
- Publisher
- Natural Sciences Publishing
- Published
- 2016-01-01
- Volume
- 2
- Issue
- 1
- Pages
- 1-11
- ISSN
- 2356-9336 (ISSN-L)
- 2356-9344
- OpenAlex
- W2740460687
- Cited by
- 540
- References
- 1
- FWCI
- 40.51
- Type
- journal article
- Language
- en
- Open access
- closed
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- Caputo, M., & Fabrizio, M. (2016). Applications of New Time and Spatial Fractional Derivatives with Exponential Kernels. Progress in Fractional Differentiation and Applications. https://doi.org/10.18576/pfda/020101
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