Abstract
The present article discovers the new soliton wave solutions and their propagation in nonlinear low-pass electrical transmission lines (NLETLs). Based on an innovative Exp-function method, multitype soliton solutions of nonlinear fractional evolution equations of NLETLs are established. The equation is reformulated to a fractional-order derivative by using the Jumarie operator. Some new results are also presented graphically to understand the real physical importance of the studied model equation. The physical interpretation of waves is represented in the form of three-dimensional and contour graphs to visualize the underlying dynamic behavior of these solutions for particular values of the parameters. Moreover, the attained outcomes are generally new for the considered model equation, and the results show that the used method is efficient, direct, and concise which can be used in more complex phenomena.
Highlights
Considerable attention from scientists and researchers during the last two decades has highlighted that fractional differential simulations provide a better understanding than classical simulations to describe the complexities of physical scenarios in this real world
For the conversion of equation (6) into an ordinary differential equation (ODE), we considered the fractional wave transformation as u(x, t) u(η)η kxα/α + ωtα/α
It is clear from this work that fractional derivative has very important role in understanding the structure of the presented nonlinear evolution equation and describes the continuous behavior of the solution wave through out the process
Summary
Considerable attention from scientists and researchers during the last two decades has highlighted that fractional differential simulations provide a better understanding than classical simulations to describe the complexities of physical scenarios in this real world. Investigation of different types of soliton solutions of fractional differential equations (FDEs) can be identified through different techniques and has been examined by many authors [5,6,7,8,9]. To the best of our knowledge, the obtained results by using mathematical modelling and analytical technique presented in this paper for nonlinear fractional evolution equation of NLETLs are new, more general, and comprise some valuable information.
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