Further innovative optical solitons of fractional nonlinear quadratic-cubic Schrödinger equation via two techniques

Arbitrary order partial differential equations involving nonlinearity have mostly been utilized to portray interior behavior of numerous real-world phenomena during the couple of years. The research about the nonlinear optical context relating to saturable law, power law, triple-power law, dual-power law, logarithm law, polynomial low and mostly visible Kerr law media is increasing at a remarkable rate. In this exploration, the space and time fractional nonlinear Schrodinger equation with the quadratic-cubic nonlinearity is taken into account for optical solitons and other solutions by means of the improved tanh method and the rational $$\left( {G^{\prime}/G} \right)$$ -expansion method. An alteration of wave variable with the assistance of conformable fractional derivative reduces the suggested equation into an ordinary differential equation. A successful adaptation of the mentioned techniques makes available plentiful solitons and other types solutions of the above equation. The originated solutions might be accommodating to analyze the underlying structures of nonlinear optics. We bring out the diverse 3-D and 2-D shapes for solitons to depict the physical appearances of the achieved solutions. The performance of the adopted methods is mentionable which claimed to be eligible for using to unravel any other nonlinear partial differential equations emerging in nature sciences.