Observations of fractional effects of [formula omitted]-derivative and M-truncated derivative for space time fractional Phi-4 equation via two analytical techniques

Abstract

The presented work deals with the investigation of space time fractional Phi-4 model which has great importance in particle and nuclear physics. Two eminent techniques, namely, the extended (G′G2)-expansion method and the modified auxiliary equation (MAE) method are utilized to construct the traveling wave solutions of fractional Phi-4 model. The fractional effects on the model are studied using the β-derivative and M-truncated derivative. The obtained results include trigonometric and hyperbolic functions with dark and periodic traveling wave behaviors. Comparison of fractional effects for the β-derivative and M-truncated derivative is illustrated through graphs by assigning particular values to fractional parameter. The obtained results will be helpful to understand the dynamical framework of time fractional Phi-4 model in the related physical phenomena.