Solution of Newell – Whitehead – Segal Equation of Fractional Order by Using Sumudu Decomposition Method

Approximate and Closed-Form Solutions of Newell-Whitehead-Segel Equations via Modified Conformable Shehu Transform Decomposition Method

“…Figure 2(a) illustrates the performance of the 5 th approximate and exact CSDM solutions of (43) for diverse values of α when ϕ � 0.10 in the interval τ ∈ [0, 1]. Indisputably, results in instances of fractional values of α converge to the results in case of α � 1.…”

“…To solve NWS equations, Benattia and Belghaba [39] employed the conformable Sumudu transform and the Adomian decomposition approach. e Sumudu decomposition approach was utilized by Ahmed and Elbadri [43] to determine approximate and definite solutions to the Caputo time-fractional NWS equations. Saadeh et al [44] obtained the approximate analytical solutions to the fractional-order NWS equations in the sense of Caputo by using the residual power series method.…”

Advantages of the Differential Equations for Solving Problems in Mathematical Physics with Symbolic Computation

“…The wave soliton pulse [6], a significant feature of nonlinearity, shows a perfect equilibrium between nonlinearity and dispersion effects. The first integral method is a powerful solution method was presented by the mathematician [7], where this method is characterized with its strength, with high accuracy and ease of application by relying on the characteristics and advantages of the differential equations as well as mathematical software in finding the exact traveling wave solutions for complex and nonlinear equations that specialized of nonlinear physical phenomena, so was applied to an important type of NLEEs and fractional equations as [8][9][10][11] with compare with other methods, for example the homotopy perturbation method [12], the generalized tanh method [13], homotopy analysis method [14], and several methods [15][16][17][18][19][20][21][22], the first integral method has proven its ability to solve various types of non-linear problems and distinguishes it from other methods by its applicable and the various solitary wave solutions that we obtain by using this method.…”

Analytical Fuzzy Analysis of a Fractional-Order Newell-Whitehead-Segel Model with Mittag-Leffler Kernel

“…For example, stripe patterns can be observed in the human fingerprints, visual cortex, and zebra skin. It is important to note that hexagonal patterns may be created using laser beam propagation across the nonlinear optical medium in a diffusion and chemical reaction model [23].…”