Abstract
The conformable fractional derivatives modified Khater (mKhat.) technique and the Adomian decomposition (AD) method is used to examine the perturbed time-fractional nonlinear Schrödinger (NLS) problem's analytical and semi-analytical wave solutions. This model describes the dynamics of optical solitons propagating via nonlinear optical fibers. For this model, we create a variety of different formulae for analytical wave solutions, including hyperbolic, trigonometric, rational, dark, brilliant, combined dark-bright, singular, combined singular, and periodic wave solutions. Additionally, the Adomian decomposition approach is utilized to evaluate the absolute error between analytical and semi-analytical wave solutions. The Hamiltonian system is used to analyze the stability of found solutions to demonstrate their suitability for implementation in the model's application.
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