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Hadamard-Type Fractional Heat Equations and Ultra-Slow Diffusions
- Source :
- Fractal and Fractional, Vol 5, Iss 48, p 48 (2021), Fractal and Fractional, Volume 5, Issue 2
- 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.
- Subjects :
- Statistics and Probability
Differential equation
inverse stable subordinators
01 natural sciences
Hadamard fractional derivatives
010104 statistics & probability
Hadamard transform
0103 physical sciences
QA1-939
Applied mathematics
0101 mathematics
010306 general physics
Mathematics
Cauchy problem
anomalous diffusions
QA299.6-433
Stochastic process
Statistical and Nonlinear Physics
Method of undetermined coefficients
Nonlinear system
Lévy processes
Time derivative
Thermodynamics
Heat equation
QC310.15-319
Analysis
Subjects
Details
- Language :
- English
- ISSN :
- 25043110
- Volume :
- 5
- Issue :
- 48
- Database :
- OpenAIRE
- Journal :
- Fractal and Fractional
- Accession number :
- edsair.doi.dedup.....4c59457a41977214d99df75534656e47