Exact Solitary Wave Solutions in Nonlinear Carbon Nanotube Composite Beams on Viscoelastic Foundations Under M-Truncated Derivative

Abstract

In this study, the nonlinear partial differential equation that governs the free vibration of a carbon nanotube composite beam is analytically investigated using the truncated M-fractional derivative. This model is a beam supported by a nonlinear viscoelastic base and reinforced by carbon nanotubes. The exact solitary wave solutions are obtained by applying the generalized exponential rational function. Consequently, we obtain new types of solitary traveling wave solutions for this model as well as innovative soliton solutions such as bright, dark, singular, trigonometric, and rational solutions with complex structures. Furthermore, we plotted 2D, 3D, and contour graphs for several stated solutions by selecting appropriate parameter values. These results suggest that a more powerful, direct, and efficient mathematical tool for locating the exact single solutions to the nonlinear partial differential equations that arise in many natural science domains, such as mathematical biology, materials physics, mathematical physics, chemistry, and fluid mechanics, is the generalized exponential rational function technique.