Subdiffusive Reaction Model of Molecular Species in Liquid Layers: Fractional Reaction-Telegraph Approach

• Main Authors: Ashraf M. Tawfik, Mohamed Mokhtar Hefny
• Format: Article
• Language: English
• Published: MDPI AG 2021-06-01
• Series: Fractal and Fractional
• Subjects: anomalous diffusion; fractional calculus; cold atmospheric plasma; plasma with liquids
• Online Access: https://www.mdpi.com/2504-3110/5/2/51

In recent years, different experimental works with molecular simulation techniques have been developed to study the transport of plasma-generated reactive species in liquid layers. Here, we improve the classical transport model that describes the molecular species movement in liquid layers via considering the fractional reaction–telegraph equation. We have considered the fractional equation to describe a non-Brownian motion of molecular species in a liquid layer, which have different diffusivities. The analytical solution of the fractional reaction–telegraph equation, which is defined in terms of the Caputo fractional derivative, is obtained by using the Laplace–Fourier technique. The profiles of species density with the mean square displacement are discussed in each case for different values of the time-fractional order and relaxation time.