Analytical Analyses for a Fractional Low-Pass Electrical Transmission Line Model with Dynamic Transition

Abstract

This research explores the solitary wave solutions, including dynamic transitions for a fractional low-pass electrical transmission (LPET) line model. The fractional-order (FO) LPET line mathematical system has yet to be published, and neither has it been addressed via the extended direct algebraic technique. A computer program is utilized to validate all of the incoming solutions. To illustrate the dynamical pattern of a few obtained solutions indicating trigonometric, merged hyperbolic, but also rational soliton solutions, dark soliton solutions, the representatives of the semi-bright soliton solutions, dark singular, singular solitons of Type 1 and 2, and their 2D and 3D trajectories are presented by choosing appropriate values of the solutions’ unrestricted parameters. The effects of fractionality and unrestricted parameters on the dynamical performance of achieved soliton solutions are depicted visually and thoroughly explored. We furthermore discuss the sensitivity assessment. We, however, still examine how our model’s perturbed dynamical framework exhibits quasi periodic-chaotic characteristics. Our investigated solutions are compared with those listed in published literature. This research demonstrates the approach’s profitability and effectiveness in extracting a range of wave solutions to nonlinear evolution problems in mathematics, technology, and science.

Exploring exact solutions for physical differential models through generalized derivatives

“…where B(w) satisfies equation (8) and Q 0 , Q 1 , and Q 2 are constant coefficients to be specified. By inserting equation (13) into equation (12), employing equation (8), and letting the coefficients of B j ( j = 0, 1, 2) to be zero, we have the following algebraic system.…”

“…Nonlinear partial conformable fractional differential equations (NPCFDEs) are very beneficial equations in many scientific fields including natural sciences and engineering. There is a lot of research done as far as the existence of accurate solutions for some famous NPCFDEs [8][9][10][11][12][13]. Some of these articles have proven their effectiveness by giving different types of accurate solutions for such equations.…”