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 4 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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Design and Implementation of Fuzzy-Fractional Wu–zhang System Using He–mohand Algorithm

QAYYUM,

AHMAD,

SOHAIL

et al. 2024

Fractals

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In recent years, fuzzy and fractional calculus are utilized for simulating complex models with uncertainty and memory effects. This study is focused on fuzzy-fractional modeling of (2+1)-dimensional Wu–Zhang (WZ) system. Caputo-type time-fractional derivative and triangular fuzzy numbers are employed in the model to observe uncertainties in the presence of non-local and memory effects. The extended He–Mohand algorithm is proposed for the solution and analysis of the current model. This approach is based on homotopy perturbation method along with Mohand transformation. Effectiveness of proposed methodology at upper and lower bounds is confirmed through residual errors. The theoretical convergence of proposed algorithm is proved alongside numerical computations. Existence and uniqueness of solution are also theoretically proved in the given paper. Current investigation considers three types of fuzzifications i.e. fuzzified equations, fuzzified conditions, and finally fuzzification in both model and conditions. Different physical aspects of WZ system profiles are analyzed through 2D and 3D illustrations at upper and lower bounds. The obtained results highlight the impact of uncertainty on WZ system in fuzzy-fractional space. Hence, the proposed methodology can be used for other fuzzy-fractional systems for better accuracy with lesser computational cost.

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

Cited by 4 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

Design and Implementation of Fuzzy-Fractional Wu–zhang System Using He–mohand Algorithm

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

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