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Hadamard-Type Fractional Heat Equations and Ultra-Slow Diffusions
- Source :
- Fractal and Fractional, Vol 5, Iss 2, p 48 (2021)
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing the classical time derivative with the Hadamard operator. The stochastic meaning of the introduced abstract differential equation is provided, and the application to the particular case of the fractional heat equation is then discussed in detail. The ultra-slow behaviour emerges from the explicit form of the variance of the random process arising from our analysis. Finally, we obtain a particular solution for the nonlinear Hadamard-diffusive equation.
Details
- Language :
- English
- ISSN :
- 25043110
- Volume :
- 5
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Fractal and Fractional
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.5e60b0e692452b8bfd8de58d4ebd57
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/fractalfract5020048