Additive Noise Effects on the Stabilization of Fractional-Space Diffusion Equation Solutions

Wael W. Mohammed, Naveed Iqbal and Thongchai Botmart
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Wael W. Mohammed: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Naveed Iqbal: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Thongchai Botmart: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Mathematics, 2022, vol. 10, issue 1, 1-14

Abstract: This paper considers a class of stochastic fractional-space diffusion equations with polynomials. We establish a limiting equation that specifies the critical dynamics in a rigorous way. After this, we use the limiting equation, which is an ordinary differential equation, to approximate the solution of the stochastic fractional-space diffusion equation. This equation has never been studied before using a combination of additive noise and fractional-space, therefore we generalize some previously obtained results as special cases. Furthermore, we use Fisher’s and Ginzburg–Landau equations to illustrate our results. Finally, we look at how additive noise affects the stabilization of the solutions.

Keywords: approximate solutions; fractional Laplacian; limiting equation; stochastic fractional-space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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