An Analytical Technique, Based on Natural Transform to Solve Fractional-Order Parabolic Equations

Agarwal, Ravi P.; Mofarreh, Fatemah; Shah, Rasool; Luangboon, Waewta; Nonlaopon, Kamsing

doi:10.3390/e23081086

Cited by 38 publications

(18 citation statements)

References 27 publications

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“…In addition, this technique does not depend upon a parameter, as required for homotopy analysis and homotopy perturbation methods. However, the solutions achieved via this technique are the same as gained by the Adomian decomposition method (for detail, see [30][31][32][33]). It must be mentioned that the Yang decomposition method is more effective than the basic Adomian decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Time-Fractional Whitham-Broer-Kaup Equations with Exponential-Decay Kernel

Yasmin¹

2022

Fractal Fract

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This paper presents the semi-analytical analysis of the fractional-order non-linear coupled system of Whitham-Broer-Kaup equations. An iterative process is designed to analyze analytical findings to the specified non-linear partial fractional derivatives scheme utilizing the Yang transformation coupled with the Adomian technique. The fractional derivative is considered in the sense of Caputo-Fabrizio. Two numerical problems show the suggested method. Moreover, the results of the suggested technique are compared with the solution of other well-known numerical techniques such as the Homotopy perturbation technique, Adomian decomposition technique, and the Variation iteration technique. Numerical simulation has been carried out to verify that the suggested methodologies are accurate and reliable, and the results are revealed using graphs and tables. Comparing the analytical and actual solutions demonstrates that the proposed approaches effectively solve complicated non-linear problems. Furthermore, the proposed methodologies control and manipulate the achieved numerical solutions in a vast acceptable region in an extreme manner. It will provide us with a simple process to control and adjust the convergence region of the series solution.

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Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Time-Fractional Whitham-Broer-Kaup Equations with Exponential-Decay Kernel

Yasmin¹

2022

Fractal Fract

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“…For these complex problems, a new technique has been used by the researchers known as fractional differential equations (FDEs). In the mathematical modeling of realworld physical problems, FDEs have been widespread due to their numerous applications in engineering and real-life sciences problems [6][7][8][9], such as economics [10], solid mechanics [11], continuum and statistical mechanics [12], oscillation of earthquakes [13], dynamics of interfaces between soft-nanoparticles and rough substrates [14], fluiddynamic traffic model [15], colored noise [16], solid mechanics [11], anomalous transport [17], and bioengineering [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Fractional‐Order Delay Differential Equations by the Numerical Method

et al. 2022

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In this study, we implemented a new numerical method known as the Chebyshev Pseudospectral method for solving nonlinear delay differential equations having fractional order. The fractional derivative is defined in Caputo manner. The proposed method is simple, effective, and straightforward as compared to other numerical techniques. To check the validity and accuracy of the proposed method, some illustrative examples are solved by using the present scenario. The obtained results have confirmed the greater accuracy than the modified Laguerre wavelet method, the Chebyshev wavelet method, and the modified wavelet-based algorithm. Moreover, based on the novelty and scientific importance, the present method can be extended to solve other nonlinear fractional-order delay differential equations.

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“…Obtaining exact analytical expressions to FDEs is exceedingly difficult, if not impossible, due to the complexity of computation involved in these equations. As a result, it is necessary to seek out some useful approximations and numerical techniques, such as the homotopy perturbation method [13], variation iteration method [14], residual power series method [15], approximate-analytical method [16], Elzaki transform decomposition method [17], Iterative Laplace transform method [18], Adomian decomposition method [19], reduced differential transform method, and others [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

The Analysis of Fractional‐Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform

et al. 2022

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In this article, we solve nonlinear systems of third order KdV Equations and the systems of coupled Burgers equations in one and two dimensions with the help of two different methods. The suggested techniques in addition with Laplace transform and Atangana–Baleanu fractional derivative operator are implemented to solve four systems. The obtained results by implementing the proposed methods are compared with exact solution. The convergence of the method is successfully presented and mathematically proved. The results we get are compared with exact solution through graphs and tables which confirms the effectiveness of the suggested techniques. In addition, the results obtained by employing the proposed approaches at different fractional orders are compared, confirming that as the value goes from fractional order to integer order, the result gets closer to the exact solution. Moreover, suggested techniques are interesting, easy, and highly accurate which confirm that these methods are suitable methods for solving any partial differential equations or systems of partial differential equations as well.

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An Analytical Technique, Based on Natural Transform to Solve Fractional-Order Parabolic Equations

Cited by 38 publications

References 27 publications

Numerical Analysis of Time-Fractional Whitham-Broer-Kaup Equations with Exponential-Decay Kernel

Numerical Analysis of Time-Fractional Whitham-Broer-Kaup Equations with Exponential-Decay Kernel

Analysis of the Fractional‐Order Delay Differential Equations by the Numerical Method

The Analysis of Fractional‐Order Nonlinear Systems of Third Order KdV and Burgers Equations via a Novel Transform

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