Optical wave solutions of perturbed time-fractional nonlinear Schrödinger equation

Explicit and exact travelling wave solutions for Hirota equation and computerized mechanization

“…The limitations of the study lie in that the method is only used for integer-order equations, potential applications to fractional derivative equations will be also interesting for practical problems [ 17 , 18 ]. This is under the scope of our future investigation.…”

A Symmetry of Boundary Functions Method for Solving the Backward Time-Fractional Diffusion Problems

“…Besides the time-fractional diffusion equation, lots of scholars have developed many schemes to cope with the time fractional Burgers' equation, like the operator splitting approach and artificial boundary method [19], the nonuniform Alikhanov formula of the Caputo time fractional derivative and Fourier spectral approximation in space [20], the L1 scheme and the local discontinuous Galerkin method [21], the Lucas polynomials coupled with finite difference method [22], the fourth-order compact difference scheme [23], the L1 implicit difference scheme based on non-uniform meshes [24], a secondorder energy stable and nonuniform time-stepping scheme [25], a collocation approach with trigonometric tension B-splines [26], the cubic B-spline functions and θ-weighted scheme [27], the local projection stabilization virtual element method [28], a compact difference scheme [29], the Caputo-Katugampola fractional derivative by extending the Laplace transform [30], and the tailored finite point method based on exponential basis [31]. For the time-fractional Schrödinger equations, lots of researchers have proposed many algorithms, like the conformable natural transform and the homotopy perturbation method [32], the conformable fractional derivatives modified Khater technique and the Adomian decomposition method [33], the Laplace Adomian decomposition method and the modified generalized Mittag-Leffler function method [34], a Caputo residual power series scheme [35], and the extended Kudryashov method [36].…”

On the exact solutions of optical perturbed fractional Schrödinger equation

“…The sub-equation method (see, [22,23]), the auxiliary equation method (see, [24]), the variational iteration method (see, [25]), the first integral method (see, [26]), F-expansion method (see, [27]), G G 2 ( ) ¢ extension method (see, [28]), He's semi inverse method (see, [29]) are some examples. The article (see, [30]) uses the modified Khater method for the solution of nonlinear Schrodinger perturbed problems and finds solutions in several different forms In optical fiber materials, article [31] uses the new sub-equation method and obtains many hyperbolic, trigonometric, and rational function exact solutions of the nonlinear perturbed Schrödinger equation with Kerr law nonlinearity. The space-time fractional perturbed nonlinear SchrÃdinger equation in nanofibers is investigated using the improved tan(f(ò)/2) extension method to obtain new exact solutions [32].…”