Document Type : Research Paper

**Author**

Department of Mathematics and Statistics University of Jaffna, Sri Lanka.

**Abstract**

In the present study, we investigate the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with three different laws of nonlinearity namely, parabolic law, quadratic-cubic law, and weak non-local law. This model governs the propagation of solitons through nonlinear optical fibers. An effective approach namely, the exp(−Φ(ξ)) expansion method is applied to construct some new soliton solutions of the governing model. Consequently, the dark, singular, rational and periodic solitary wave solutions are successfully revealed. The comparisons with other results are also presented. In addition, the dynamical structures of obtained solutions are presented through 3D and 2D plots.

**Keywords**

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July 2022

Pages 701-715

**Receive Date:**30 June 2021**Revise Date:**05 October 2021**Accept Date:**16 October 2021**First Publish Date:**25 October 2021