Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis

Communication systems, especially radio frequency and microwave systems are significant to global society. Optimizing these systems involves using the telegraph equation to determine power and signal losses. This equation is essential in theoretical, mathematical, and nonlinear research involving pl...

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Main Authors: Usman Younas, Jan Muhammad, Muhammad Amin S. Murad, D.K. Almutairi, Aziz Khan, Thabet Abdeljawad
Format: Article
Language:English
Published: Elsevier 2025-03-01
Series:Results in Engineering
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Online Access:http://www.sciencedirect.com/science/article/pii/S2590123025005675
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author Usman Younas
Jan Muhammad
Muhammad Amin S. Murad
D.K. Almutairi
Aziz Khan
Thabet Abdeljawad
author_facet Usman Younas
Jan Muhammad
Muhammad Amin S. Murad
D.K. Almutairi
Aziz Khan
Thabet Abdeljawad
author_sort Usman Younas
collection DOAJ
description Communication systems, especially radio frequency and microwave systems are significant to global society. Optimizing these systems involves using the telegraph equation to determine power and signal losses. This equation is essential in theoretical, mathematical, and nonlinear research involving plasma physics, and is used to describe communication lines, the expansion of circulating blood pressure waves, and the random motion of one-dimensional bugs. This study investigates the dynamic behavior of the fractional telegraph equation with M-fractional derivative. The wave transformation is applied, and the model is transferred to an ordinary differential equation. Furthermore, two recently developed integration tools known as the generalized Arnous approach and modified F-expansion method have been adopted for analyzing the studied model. A variety of solitary wave solutions are extracted in different forms. Moreover, the fractional parametric effect has been observed graphically in various plots depicting wave dynamics. Another aspect of this study is to explore the telegraph by the chaotic and sensitivity analysis. For this purpose, the Galilean transformation is applied, and a variety of graphs in 2D phase portraits and time-series analyses have been sketched. The algorithms of the proposed techniques are outstanding allowing them to resolve exact soliton solutions in complex nonlinear structures with high precision in an efficient and effective manner. The results obtained may enhance the understanding of nonlinear system dynamics and validate current methods, significantly contributing to the fields of nonlinear science and wave phenomena. The analysis is expected to benefit numerous scientific models and related issues, making a significant contribution to nonlinear systems.
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spelling doaj-art-75d16bf73ee544b3adc67e516b2fb3e42025-08-20T01:47:28ZengElsevierResults in Engineering2590-12302025-03-012510448910.1016/j.rineng.2025.104489Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysisUsman Younas0Jan Muhammad1Muhammad Amin S. Murad2D.K. Almutairi3Aziz Khan4Thabet Abdeljawad5Department of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, No. 99 Shangda Road, Shanghai 200444, ChinaDepartment of Mathematics, College of Science, University of Duhok, Duhok, IraqDepartment of Mathematics, College of Science Al-Zulfi, Majmaah University, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Saudi ArabiaDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India; Department of Mathematics and Sciences, Prince Sultan University, Saudi Arabia; Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Garankuwa, Medusa 0204, South Africa; Corresponding author at: Department of Mathematics and Sciences, Prince Sultan University, Saudi Arabia.Communication systems, especially radio frequency and microwave systems are significant to global society. Optimizing these systems involves using the telegraph equation to determine power and signal losses. This equation is essential in theoretical, mathematical, and nonlinear research involving plasma physics, and is used to describe communication lines, the expansion of circulating blood pressure waves, and the random motion of one-dimensional bugs. This study investigates the dynamic behavior of the fractional telegraph equation with M-fractional derivative. The wave transformation is applied, and the model is transferred to an ordinary differential equation. Furthermore, two recently developed integration tools known as the generalized Arnous approach and modified F-expansion method have been adopted for analyzing the studied model. A variety of solitary wave solutions are extracted in different forms. Moreover, the fractional parametric effect has been observed graphically in various plots depicting wave dynamics. Another aspect of this study is to explore the telegraph by the chaotic and sensitivity analysis. For this purpose, the Galilean transformation is applied, and a variety of graphs in 2D phase portraits and time-series analyses have been sketched. The algorithms of the proposed techniques are outstanding allowing them to resolve exact soliton solutions in complex nonlinear structures with high precision in an efficient and effective manner. The results obtained may enhance the understanding of nonlinear system dynamics and validate current methods, significantly contributing to the fields of nonlinear science and wave phenomena. The analysis is expected to benefit numerous scientific models and related issues, making a significant contribution to nonlinear systems.http://www.sciencedirect.com/science/article/pii/S2590123025005675Modified F-expansion methodGeneralized Arnous methodTelegraph equationM-fractional derivativesGalilean transformation
spellingShingle Usman Younas
Jan Muhammad
Muhammad Amin S. Murad
D.K. Almutairi
Aziz Khan
Thabet Abdeljawad
Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis
Results in Engineering
Modified F-expansion method
Generalized Arnous method
Telegraph equation
M-fractional derivatives
Galilean transformation
title Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis
title_full Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis
title_fullStr Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis
title_full_unstemmed Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis
title_short Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis
title_sort investigating the truncated fractional telegraph equation in engineering solitary wave solutions chaotic and sensitivity analysis
topic Modified F-expansion method
Generalized Arnous method
Telegraph equation
M-fractional derivatives
Galilean transformation
url http://www.sciencedirect.com/science/article/pii/S2590123025005675
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