Investigation of New Optical Solutions for the Fractional Schrödinger Equation with Time-Dependent Coefficients: Polynomial, Random, Trigonometric, and Hyperbolic Functions

The fractional Schrödinger equation with time-dependent coefficients (FSE-TDCs) is taken into consideration here. The mapping method and the (G′/G)-expansion method are applied to generate new bright solutions, kink solutions, dark optical solutions, singular solutions, periodic solutions, and others. Because the Schrödinger equation is widely employed in quantum computers, quantum mechanics, physics, engineering, and chemistry, the solutions developed can be utilized to examine a wide range of important physical phenomena. In addition, we illustrate the influence of the coefficients, when these coefficients have specific values, such as random, polynomial, trigonometric, and hyperbolic functions, on the exact solutions of FSE-TDCs. Also, we show the influence of fractional-order derivatives on the obtained solutions.