Exact special solutions of space-time fractional Cahn-Allen equation by beta and M-truncated derivatives

In this paper, we consider the nonlinear space-time fractional form of Cahn-Allen equation (FCAE) with beta and M-truncated derivatives. Cahn-Allen equation (CAE) is commonly used in many problems of physics and engineering, such as, solidification problems, phase separation in iron alloys and others. We apply the improved tan(?(?)2)-expansion method (ITEM). We obtain four types of traveling wave solutions, including, trigonometric, hyperbolic, rational and exponential function solutions. We demonstrate some of the extracted solutions using definitions of the beta (BD) and M-truncated derivatives (MTD) to understand their dynamical behavior. We observe the fractional effects of the aforementioned derivatives on the related physical phenomena up to possible extent.