Abstract
Abstract The fundamental objective of this article is to find exact solutions to the stochastic fractional-space Allen–Cahn equation, which is derived in the Itô sense by multiplicative noise. The exact solutions to this equation are required since it appears in many discipline areas including plasma physics, quantum mechanics and mathematical biology. The tanh–coth method is used to generate new hyperbolic and trigonometric stochastic and fractional solutions. The originality of this study is that the results produced here expand and improve on previously obtained results. Furthermore, we use Matlab package to display 3D surfaces of analytical solutions derived in this study to demonstrate the effect of stochastic term on the solutions of the stochastic-fractional-space Allen–Cahn equation.
Highlights
Fractional derivatives have attracted a lot of attention in recent decades due to their possible applications in aOn the other hand, random perturbations arise from many natural sources in the practically physical system
Some related research on approximate solutions of fractional differential equations with stochastic term have been explored such as Liu and Yan [13], Mohammed [14], Zou [15,16], Ahmad et al [17,18], Li and Yang [19], Kamrani [20] and Taheri et al [21]
The fractional-space Allen–Cahn equation induced by multiplicative noise in the Itô sense is taken into account as follows:
Summary
Random perturbations arise from many natural sources in the practically physical system They cannot be denied and the presence of noise can lead to some statistical properties and important phenomena. The fractional-space Allen–Cahn equation induced by multiplicative noise in the Itô sense is taken into account as follows:. The purpose of this article is to find the exact solutions of the stochastic fractional-space Allen–Cahn Eq (1) derived by a one-dimensional multiplicative white noise by using the tanh–coth method. The obtained solutions would be quite useful in explaining certain exciting physical phenomena This is the first work to provide exact solutions to the stochastic fractional-space Allen–Cahn Eq (1).
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