Abstract
This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF–ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The aim of this paper is to propose a simple and robust implicit unconditionally stable finite difference method for solving the TF–ADR equations. The numerical results show that the proposed method is efficient, reliable and easy to implement from a computational viewpoint and can be employed for engineering sciences problems.
Highlights
In the last years, the fractional differential equations (FDEs) have attracted considerable interest by the numerous researchers
For a better understanding of the historical aspects of fractional calculus, the analytical properties of the fractional differential equations, and the difficulties associated with them, the readers are referred to the books [2,3]
By comparison with the experimental and numerical results available in the specialized literature [38,40,41,44], we can conclude that the proposed computational method is an efficient and accurate tool in the characterization and validation of solution for the packed bed columns model governed by a time-fractional advection-diffusion-reaction equation
Summary
The fractional differential equations (FDEs) have attracted considerable interest by the numerous researchers. We consider a class of mathematical models that, in recent years, has been a great deal of interest in fractional differential equations These equations have important applications in various areas such as nonlinear hydrodynamics, population dynamic, biophysics, engineering, neurosciences, polymer physics, laser physics, plasma physics, surface physics, pattern formation, psychology, and marketing. Combining physical and chemical processes into the same mathematical model, we obtain the time-fractional advection-diffusion-reaction (TF–ADR) equations used to describe a wide variety of nonlinear processes arising in many fields of the applied sciences. Determining the exact solution to characterize the flowing fluid through one of these structures becomes impossible For this reason, numerical solutions of mathematical models have received a great attention over the years.
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