Analytical Approach to Fractional Order Newell-Whitehead-Segel Equations by Sumudu transform Iterative Method (original) (raw)

A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation

Boundary value problems, 2024

This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell-Whitehead-Segel equation plays a significant role. The findings indicate that the outcomes derived from the tables yield superior results compared to the existing LTDM in the literature. Maple is utilized to depict three-dimensional surfaces and find numerical values that are displayed in a table.

Analytical Analysis of Fractional-Order Newell-Whitehead-Segel Equation: A Modified Homotopy Perturbation Transform Method

Journal of Function Spaces

This paper has applied a hybrid method called the homotopy perturbation transformation technique to solve fractional-order Newell-Whitehead-Segel equations. First, we used the Yang transformation to the given problem, and then, the homotopy perturbation technique was implemented to complete the procedure of the suggested method. The proposed method is simplified and requires a small calculation to achieve the solution to the targeted problem. Moreover, the derived results are in close contact with the exact results of the given models. Three examples are solved to confirm and show the feasibility of the present scenario. The findings obtained from the proposed procedure have also been in excellent alignment with other technique outcomes. It is shown that the proposed approach is effective, consistent, and straightforward to apply to various relevant problems in engineering and science.

Asymptotic-sequentially solution style for the generalized Caputo time-fractional Newell–Whitehead–Segel system

Advances in Difference Equations, 2019

The Caputo fractional version of the generalized Newell-Whitehead-Segel model is considered. We introduced a numerical scheme to solve analytically the proposed application. We updated the style of the generalized Taylor series for a reliable treatment of the time-fractional derivative. The effect of the fractional derivative is explored on the obtained solutions for different cases of the problem. A sequential-asymptotic phenomenon has been observed upon varying the order of the fractional derivative from no-memory "α = 0" to full-memory "α = 1".

Solution of Newel-Whitehead-Segel Equation Using Conformable Fractional Sumudu Decomposition Method

Journal of Science and Arts

In the present paper, a numerical method is proposed to solve the time fractional Newel-Whitead-Segel equation subject to initial condition. This method is based d on the unification of conformable Sumudu transform (CST) and Adomian decomposition method (ADM), and then it is used to find the analytical solutions of linear-nonlinear fractional PDE’s. The test examples are given for illustration

A new application of conformable Laplace decomposition method for fractional Newell-Whitehead-Segel equation

AIMS Mathematics, 2020

In this study, it is the first time that conformable Laplace decomposition method (CLDM) is applied to fractional Newell-Whitehead-Segel (NWS) equation which is one of the most significant amplitude equations in physics. The method consists of the unification of conformable Laplace transform and Adomian decomposition method (ADM) and it is used for finding approximate analytical solutions of linear-nonlinear fractional PDE's. The results show that this CLDM is quite powerful in solving fractional PDE's.

Coupled FCT-HP for Analytical Solutions of the Generalized Timefractional Newell-Whitehead-Segel Equation

WSEAS Transactions on Systems and Control archive, 2018

This paper considers the generalized form of the time-fractional Newell-Whitehead-Segel model (TFNWSM) with regard to exact solutions via the application of Fractional Complex Transform (FCT) coupled with He’s polynomials method of solution. This is applied to two forms of the TFNWSM viz: nonlinear and linear forms of the time-fractional NWSM equation whose derivatives are based on Jumarie’s sense. The results guarantee the reliability and efficiency of the proposed method with less computation time while still maintaining high level of accuracy.

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

Mathematical Problems in Engineering

In this study, we introduced a novel scheme to attain approximate and closed-form solutions of conformable Newell-Whitehead-Segel (NWS) equations, which belong to the most consequential amplitude equations in physics. The conformable Shehu transform (CST) and the Adomian decomposition method (ADM) are combined in the proposed method. We call it the conformable Shehu decomposition method (CSDM). To assess the efficiency and consistency of the recommended method, we demonstrate 2D and 3D graphs as well as numerical simulations of the derived solutions. As a result, CSDM demonstrates that it is a useful and simple mathematical tool for getting approximate and exact analytical solutions to linear-nonlinear fractional partial differential equations (PDEs) of the given kind. The convergence and absolute error analysis of the series solutions is also offered.

Application of Fractional Residual Power Series Algorithm to Solve Newell-Whitehead-Segel Equation of Fractional Order

Symmetry, 2019

The Newell-Whitehead-Segel equation is one of the most nonlinear amplitude equations that plays a significant role in the modeling of various physical phenomena arising in fluid mechanics, solid-state physics, optics, plasma physics, dispersion, and convection system. In this analysis, a recent numeric-analytic technique, called the fractional residual power series (FRPS) approach, was successfully employed in obtaining effective approximate solutions to the Newell-Whitehead-Segel equation of the fractional sense. The proposed algorithm relies on a generalized classical power series under the Caputo sense and the concept of an error function that systematically produces an analytical solution in a convergent fractional power series form with accurately computable structures, without the need for any unphysical restrictive assumptions. Meanwhile, two illustrative applications are included to show the efficiency, reliability, and performance of the proposed technique. Plotted and numerical results indicated the compatibility between the exact and approximate solution obtained by the proposed technique. Furthermore, the solution behavior indicates that increasing the fractional parameter changes the nature of the solution with a smooth sense symmetrical to the integer-order state.

A Novel Analytical Approach for Solving Time-Fractional Diffusion Equations

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH

This article investigates the approximate analytical solutions of the time-fractional diffusion equations using a novel analytical approach, namely the Sumudu transform iterative method. The time-fractional derivatives are considered in the Caputo sense. The analytical solutions are found in closed form, in terms of Mittag-Leffler functions. Furthermore, the findings are shown graphically, and the solution graphs demonstrate a strong relationship between the approximate and exact solutions.