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This study investigates soliton solutions and dynamical behavior in the nonlinear telegraph equation using Katugampola fractional derivatives, which generalize both Riemann-Liouville and Hadamard fractional calculus. The researchers derive analytical soliton solutions and analyze the phase-space dynamics to understand wave propagation characteristics in fractional-order systems. Stability analysis is performed to determine conditions under which these soliton solutions remain robust, providing insights into the mathematical structure of fractional differential equations modeling signal transmission.
Why it matters
The telegraph equation models signal propagation in electrical transmission lines and wave phenomena in various physical systems. Understanding its behavior under fractional-order derivatives could improve modeling of dissipative and memory-dependent processes in telecommunications, electromagnetic wave transmission, and anomalous diffusion phenomena in complex media.
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