Mitigating Internet bottleneck with fractional temporal evolution of optical solitons having quadratic–cubic nonlinearity

A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

“…Many numerical and analytical techniques have been suggested for the solutions of linear and nonlinear FPDEs [3]. Some emerging analytical approximate approaches for FDEs are homotopy analysis method (HAM) [4], variational iteration method (VIM) [5], generalized fractional Taylor series method [6][7][8][9], iterative fractional power series system to solve a number of fractional integrodifferential equations [10]; using the Kudryashov technique and trial solution technique, we obtained traveling wave approaches to a fractional, nonlinear Schrodinger problem [11][12][13]; analytical solution to solve a particular homogeneous time-invariant fractional original value problem [14]; Taylor power series solution method is used to obtain approximate 2D time-space fractional diffusion, wave-like, telegraph, time-fractional Phi-4 equation, and Burger models from both closed-form and supportive series alternatives [15,16]; fractional temporal evolution of optical solitons [17], fractional generalized reaction Duffing model by generalized projective Riccati equation method [18], ternary-fractional differential transform [19], Adomian decomposition method (ADM) [20], and homotopy perturbation method (HPM) [21].…”

The new extended rational SGEEM for construction of optical solitons to the (2+1)–dimensional Kundu–Mukherjee–Naskar model

“…This area has drawn the attention of many scientists for more than two decades. Different computational methods have been used to reveal solutions of various type of NLEEs such as the modified exp(−Ψ(η))-expansion function method [7][8][9], the first integral method [10,11], the improved Bernoulli sub-equation function method [12,13], the trial solution method [14,15], the new auxiliary equation method [16], the extended simple equation method [17], the solitary wave ansatz method [18], the functional variable method [19] and several others [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Numerical solutions of fractional Boussinesq-Whitham-Broer-Kaup and diffusive Predator-Prey equations with conformable derivative

“…There are some common methods that are used to obtain approximate or analytical solutions of nonlinear fractional ordinary and partial differential equations in the literature [28,29,30,31,32,33,34,35,36,37]. These methods include, Laplace analysis method (LAM) [15] for the constant coefficient fractional differential equations, Adomian decomposition method (ADM) [13] for the dynamics of the fractional giving up smoking model of fractional order, homotopy perturbation method (HPM) [25] for the nonlinear fractional Schrödinger equation, homotopy analysis method (HAM) [18] for the conformable fractional Nizhnik-Novikov-Veselov system, differential transformation method (DTM) [19] for the convergence of fractional power series, Elzaki projected differential transform method [22] for system of linear and nonlinear fractional partial differential equations and perturbation-iteration algoritm (PIA) [20] for ordinary fractional differential equations.…”