Optical solitons of space-time fractional Fokas–Lenells equation with two versatile integration architectures

Abstract

Abstract Nonlinear Schrödinger’s equation and its variation structures assume a significant job in soliton dynamics. The soliton solutions of space-time fractional Fokas–Lenells equation with a relatively new definition of local M-derivative have been recovered by utilizing improved $\tan (\frac{\phi (\eta )}{2})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>tan</mml:mo> <mml:mo>(</mml:mo> <mml:mfrac> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>η</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>)</mml:mo> </mml:math> -expansion method and generalized projective Riccati equation method. The obtained solutions are periodic, dark, bright, singular, rational, along with few forms of combo-soliton solutions. These solutions are given under constraints conditions which ensure their existence. The impact of local fractional parameter is featured by its graphical portrayal. 2D and 3D diagrams are drawn to illustrate the efficacy of the conformable fractional order on the behavior of some of those solutions. The secured solutions of this model have dynamic and significant justifications for some real-world physical occurrences. Our study shows that the suggested schemes are effective, reliable, and simple for solving different types of nonlinear differential equations.