Abstract
The nonlinear conformable fractional Schrödinger–Hirota (NCFSH) equation, describing the propagation of optical solitons in a dispersive optical fibre, is considered and its exact solutions are investigated. Abundant solutions including dark, bright and singular solutions have been obtained by two distinct methods, namely direct method and trial equation method. These methods provide a direct and efficient strategy for the NCFSH equation. The solutions have been simulated by graphs to check the types of solitons and their dynamical behaviours. With back substitution using Mathematica, all the solutions have been verified. Obtaining optical solutions to the proposed equation will play a fundamental role due to the applications in quantum mechanics, fluid dynamics, nonlinear optics and various other branches of mathematical physics.
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