Modified Modelling for Heat Like Equations within Caputo Operator

Khan, Hassan; Khan, Adnan; Al-Qurashi, Maysaa; Shah, Rasool; Băleanu, Dumitru

doi:10.3390/en13082002

Cited by 26 publications

(22 citation statements)

References 43 publications

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“…Dealing with the difficulties of computations in these equations make obtaining exact analytic solutions of FDEs extremely difficult, if not impossible. Many scholars have solved the numerical and analytical methods, such as the variation iteration technique [25], homotopy perturbation technique [26], approximate analytical technique [27], residual power series technique [28], iterative Laplace transformation technique [29], Elzaki decomposition technique [30], reduced differential technique [31] and Adomian decomposition technique [32].…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Fractional Coupled Burgers and Hirota–Satsuma KdV Equations via Analytical Techniques

Yasmin

Iqbal

2022

Symmetry

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This paper applies modified analytical methods to the fractional-order analysis of one and two-dimensional nonlinear systems of coupled Burgers and Hirota–Satsuma KdV equations. The Atangana–Baleanu fractional derivative operator and the Elzaki transform will be used to solve the proposed problems. The results of utilizing the proposed techniques are compared to the exact solution. The technique’s convergence is successfully presented and mathematically proven. To demonstrate the efficacy of the suggested techniques, we compared actual and analytic solutions using figures, which are in strong agreement with one another. Furthermore, the solutions achieved by applying the current techniques at different fractional orders are compared to the integer order. The proposed methods are appealing, simple, and accurate, indicating that they are appropriate for solving partial differential equations or systems of partial differential equations.

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Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Fractional Coupled Burgers and Hirota–Satsuma KdV Equations via Analytical Techniques

Yasmin

Iqbal

2022

Symmetry

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“…To handle partial differential equations (PDEs), having order fraction is of physical importance, and effective, trustworthy, and appropriate numerical methods are required [12][13][14]. Several major strategies have been utilized in this regard, including the fractional operational matrix method (FOMM) [15], Elzaki transform decomposition method (ETDM) [16,17], homotopy analysis method (HAM) [18], homotopy perturbation method (HPM) [19,20], iterative Laplace transform method [21], and variational iteration method (FVIM) [22].…”

Section: Introductionmentioning

confidence: 99%

Fractional-View Analysis of Space-Time Fractional Fokker-Planck Equations within Caputo Operator

Alshammari

Iqbal

Yar

2022

Journal of Function Spaces

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In this article, we investigate the fractional-order Fokker-Planck equations with the help of the Yang transform decomposition method (YTDM). The YTDM combines Yang transform, Adomian decomposition method, and Adomian polynomials into one method. In the Caputo sense, fractional derivatives of space and time are studied. The convergent series form solution demonstrates the method’s efficiency in resolving several types of fractional differential equations. Compared to other methods of finding approximate and exact solutions for nonlinear partial differential equations, this technique is more efficient and time-consuming.

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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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Modified Modelling for Heat Like Equations within Caputo Operator

Cited by 26 publications

References 43 publications

A Comparative Study of the Fractional Coupled Burgers and Hirota–Satsuma KdV Equations via Analytical Techniques

A Comparative Study of the Fractional Coupled Burgers and Hirota–Satsuma KdV Equations via Analytical Techniques

Fractional-View Analysis of Space-Time Fractional Fokker-Planck Equations within Caputo Operator

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

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