Successive Approximation Method for Solving Wu-Zhang Systems of (1   1) Dimensional

Al-Rozbayani, Abdulghafor M.; Shammar, Abdulbaset H.

doi:10.4236/oalib.1106601

Cited by 3 publications

(1 citation statement)

References 2 publications

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“…It is one of the most significant topics for mathematical physics to obtain the exact solutions. In the recent years, many authors find the numerical and analytical solution of WZ equation by using various methods, for illustration, the first integral method, 1 Adomian decomposition, 2 modified adomian decomposition method, 3 quintic method, 2 septic spline methods, 2 homotopy perturbation method (HPM), 4 extended tanh method, 5 exp-function method, 5 the exponential rational function method, 6 successive approximation method, 7 modified variation iteration method, 8 extended trial equation method, 9 and dynamical system method. 10 The nonlinear phenomenon plays a vital role in physics and applied mathematics.…”

Section: Introductionmentioning

confidence: 99%

An analytical approach to solve the fractional‐order (2 + 1)‐dimensional Wu–Zhang equation

Patel¹,

Patel

2022

Math Methods in App Sciences

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This paper considers time‐fractional false(2+1false)$$ \left(2+1\right) $$‐dimensional Wu–Zhang nonlinear system of partial differential equation describing a long dispersive wave. An approximate analytical solution of the dispersion relation of the long wave has been obtained by the fractional reduced differential transform method (FRDTM). The effect of fractional‐order α$$ \alpha $$ on the wave profile of the solution is discussed graphically and comparing the exact solution of Wu–Zhang equation when α=1$$ \alpha =1 $$. The result shows that the present method reveals the effectiveness, efficiency, and reliability of computed mathematical results to easily solve the fractional‐order Wu–Zhang (WZ) system of differential equations.

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Section: Introductionmentioning

confidence: 99%

An analytical approach to solve the fractional‐order (2 + 1)‐dimensional Wu–Zhang equation

Patel¹,

Patel

2022

Math Methods in App Sciences

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Unveiling new insights: taming complex local fractional Burger equations with the local fractional Elzaki transform decomposition method

Alhamzi,

Prasad,

Alkahtani

et al. 2024

Front. Appl. Math. Stat.

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This study aims to address the difficulties in solving coupled generalized non-linear Burger equations using local fractional calculus as a framework. The methodology used in this work, particularly in the area of local fractional calculus, combines the Elzaki transform with the Adomian decomposition method. This combination has proven to be a highly effective strategy for addressing non-linear partial differential equations within the local fractional context, which finds numerous practical applications. The proposed method offers a systematic and easily understandable procedure for tackling both linear and non-linear partial differential equations (PDEs). It provides an easy-to-follow path to solve these problems. We offer a real-world example that exhibits the method's successful use in resolving issues to corroborate its efficacy. The obtained solution is visually represented to illustrate the practical utility of this approach.2010 Mathematics Subject Classification34A34, 65M06, 26A33.

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Iterative solution of the fractional Wu-Zhang equation under Caputo derivative operator

Yasmin,

Alderremy,

Shah

et al. 2024

Front. Phys.

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In this study, we employ the effective iterative method to address the fractional Wu-Zhang Equation within the framework of the Caputo Derivative. The effective iterative method offers a practical approach to obtaining approximate solutions for fractional differential equations. We seek to provide insights into its solution and behavior by applying this method to the Wu-Zhang Equation. Through numerical analysis and the presentation of relevant tables and Figures, we demonstrate the accuracy and efficiency of this method in solving the fractional Wu-Zhang Equation. This research contributes to the understanding and solution of fractional-order differential equations and their applications in various scientific and engineering domains.

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Successive Approximation Method for Solving Wu-Zhang Systems of (1 1) Dimensional

Cited by 3 publications

References 2 publications

An analytical approach to solve the fractional‐order (2 + 1)‐dimensional Wu–Zhang equation

An analytical approach to solve the fractional‐order (2 + 1)‐dimensional Wu–Zhang equation

Unveiling new insights: taming complex local fractional Burger equations with the local fractional Elzaki transform decomposition method

Iterative solution of the fractional Wu-Zhang equation under Caputo derivative operator

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