Abstract
In this work, we are investigating a series of new optical soliton solutions to the perturbed nonlinear Schrödinger equation (PNLSE) having the form of kerr law nonlinearity with conformable space-time fractional. Thereby, two relevant integration tools known as new extended direct algebraic method and extended hyperbolic function method are applied to obtain varieties of optical soliton solutions. The series of soliton solutions with fractional derivative order obtained by these methods can be classified as complex trigonometric and hyperbolic functions as well as other elementary functions. Furthermore, conditions for validity of the obtained analytical solutions, graphical illustration (2-D, 3-D) point out the impact of the fractional-order used.
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