Solitary wave solution to the space–time fractional modified Equal Width equation in plasma and optical fiber systems

Abstract

Nonlinear fractional evolution equations play a crucial role in characterizing assorted complex nonlinear phenomena observed in different scientific fields, including plasma physics, quantum mechanics, elastic media, nonlinear optics, surface water waves, nonlinear dynamics, molecular biology, and some other domains. In this study, we investigate diverse solitary wave solutions to the space–time fractional modified Equal Width equation, focusing on their significance for wave propagation behaviors in plasma and optical fiber systems. Two effective approaches, namely the improved Bernoulli sub-equation function and the new generalized (G′/G)-expansion methods are exploited. A fractional wave transformation technique is employed to convert the fractional-order equation into an ordinary differential equation. The solitary wave solutions obtained in terms of exponential, hyperbolic, rational, and trigonometric functions, have wide applications in various nonlinear phenomena. The 3D, spherical, contour, and vector plots are presented to elucidate the physical implications of the obtained solutions for specific parameter values. The soliton structures reveal various wave types, including bell-shaped, multi-soliton, kink, single soliton, anti-bell-shaped, periodic soliton, compacton, and other types for definite values of the free parameters. We compare the attained solutions with the solutions available in the literature to demonstrate the feasibility of the solutions. It is observed that both approaches are efficient, straightforward, and significant for investigating diverse nonlinear models that modulate complex phenomena.