Time Fractional Differential Equation Model With Random Derivative Order
Keyword(s):
This paper proposes a new type of fractional differential equation model, named time fractional differential equation model, in which noise term is included in the time derivative order. The new model is applied to anomalous relaxation and diffusion processes suffering noisy field. The analysis and numerical simulation results show that our model can well describes the feature of these processes. We also find that the scale parameter and the frequency of the noise play a crucial role in the behaviors of these systems. At the end, we recognize some potential applications of this new model.
2017 ◽
Vol 102
◽
pp. 473-485
◽
2012 ◽
Vol 64
(10)
◽
pp. 3267-3275
◽
2019 ◽
Vol 2019
(1)
◽
2021 ◽
Vol 1952
(4)
◽
pp. 042089
2006 ◽
Vol 2006
◽
pp. 1-18
◽