Analytical investigation of fractional-order Newell-Whitehead-Segel equations via a novel transform

Areshi, Mounirah; Khan, Adnan; Shah, Rasool; Nonlaopon, Kamsing

doi:10.3934/math.2022385

Cited by 76 publications

(26 citation statements)

References 29 publications

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“…Using the Sumudu transform method, Gao et al [53] discovered the analytic results to several fractional ordinary differential equations. Coupled with the HPM, the Sumudu transformation method is used to explore the fractional population biological models [54]. Srivastava et al [55] initially introduce and define the fractional local Sumudu transformation of a function f (x) as follows:…”

Section: Fractional Local Sumudu Transformationmentioning

confidence: 99%

Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media

et al. 2022

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This paper investigates the fractional local Poisson equation using the homotopy perturbation transformation method. The Poisson equation discusses the potential area due to a provided charge with the possibility of area identified, and one can then determine the electrostatic or gravitational area in the fractal domain. Elliptic partial differential equations are frequently used in the modeling of electromagnetic mechanisms. The Poisson equation is investigated in this work in the context of a fractional local derivative. To deal with the fractional local Poisson equation, some illustrative problems are discussed. The solution shows the well-organized and straightforward nature of the homotopy perturbation transformation method to handle partial differential equations having fractional derivatives in the presence of a fractional local derivative. The solutions obtained by the defined methods reveal that the proposed system is simple to apply, and the computational cost is very reliable. The result of the fractional local Poisson equation yields attractive outcomes, and the Poisson equation with a fractional local derivative yields improved physical consequences.

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Section: Fractional Local Sumudu Transformationmentioning

confidence: 99%

Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media

et al. 2022

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“…Many processes in engineering, physics, chemistry, and other areas can be accurately represented by models based on fractional calculus. Furthermore, fractional calculus is used to simulate the frequency-dependent damping behavior of several viscoelastic materials [6,7], economics [8], and the dynamics of nano-particle-substrate interfaces [9].…”

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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“…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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Analytical investigation of fractional-order Newell-Whitehead-Segel equations via a novel transform

Cited by 76 publications

References 29 publications

Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media

Analysis of the Fractional-Order Local Poisson Equation in Fractal Porous Media

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

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