a periodic solution of the newell-whitehead-segel (nws) wave ‎equation via fractional calculus

The newell-whitehead-segel (nws) equation is one of the most significant amplitude equations with a wider practical applications in engineering and applied physics. it describes several line patterns; for instance, see lines from seashells and ripples in the sand. in addition, it has several applications in mathematical, chemical, and mechanical physics, as well as bio-engineering and fluid mechanics. therefore, the current research is concerned with obtaining an approximate periodic solution of a nonlinear dynamical nws wave model at three different powers. the fractional calculus via the riemann-liouville is adopted to calculate an analytical periodic approximate solution. the analysis aims to transform the original partial differential equation into a nonlinear damping duffing oscillator. then, the latter equation has been solved by utilizing a modified homotopy perturbation method (hpm). the obtained results revealed that the present technique is a powerful, promising, and effective one to analyze a class of damping nonlinear equations that appears in physical and engineering situations.