Numerical investigation for Caputo-Fabrizio fractional Riccati and Bernoulli equations using iterative reproducing kernel method

Momani, Shaher; Djeddi, Nadir; Al‐Smadi, Mohammed; Al‐Omari, Shrideh

doi:10.1016/j.apnum.2021.08.005

Cited by 54 publications

(14 citation statements)

References 45 publications

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“…Using linearization, successive, or perturbation methods, only approximate solutions can be obtained. Iterative Laplace transform method [10], Adomian decomposition method [11], Homotopy analysis method [12], operational matrix method [13], fractional differential transform method [14], Fourier transform technique [15], operational calculus method [16], Variational iteration method [17], Sumudu transform method [18], multistep generalised differential transform method [19], iterative reproducing kernel method [20], Homotopy perturbation method [21], and Numerical multistep method [22].…”

Section: Introductionmentioning

confidence: 99%

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

Tchier¹,

Khan²,

Khan³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations' solutions using the Caputo operator with Laplace residual power series method. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem. Because of the simple implementation, the present technique can be extended to solve other important fractional order problems.

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Section: Introductionmentioning

confidence: 99%

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

Tchier¹,

Khan²,

Khan³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

show abstract

“…Numerous approaches have been introduced and implemented to gain such solutions. For instance, reproducing the kernel Hilbert space method [12,13], multistep approach [14,15], residual power series method [16], Riccati-Bernoulli sub-ordinary differential equation Sub-ODE technique (RBSODET) [17], unified method [18], modified simple equation method [19], and several others [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

On a Class of Partial Differential Equations and Their Solution via Local Fractional Integrals and Derivatives

2022

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This article investigates the local fractional generalized Kadomtsev–Petviashvili equation and the local fractional Kadomtsev–Petviashvili-modified equal width equation. It presents traveling-wave transformation in a nondifferentiable type for the governing equations, which translate them into local fractional ordinary differential equations. It also investigates nondifferentiable traveling-wave solutions for certain proposed models, using an ansatz method based on some generalized functions defined on fractal sets. Several interesting graphical representations as 2D, 3D, and contour plots at some selected parameters are presented, by considering the integer and fractional derivative orders to illustrate the physical naturality of the inferred solutions. Further results are also introduced in some details.

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“…From 1980, Cui and co-workers [33,34] have been pioneers and beginners in the numerical analysis of linear and nonlinear problems using the "reproducing kernel Hilbert space method". Recently, a lot of research has been done to solve several linear and nonlinear problems using the theory of reproducing kernel [35][36][37][38][39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation

2022

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In this paper, we focus on the development and study of the finite difference/pseudo-spectral method to obtain an approximate solution for the time-fractional diffusion-wave equation in a reproducing kernel Hilbert space. Moreover, we make use of the theory of reproducing kernels to establish certain reproducing kernel functions in the aforementioned reproducing kernel Hilbert space. Furthermore, we give an approximation to the time-fractional derivative term by applying the finite difference scheme by our proposed method. Over and above, we present an appropriate technique to derive the numerical solution of the given equation by utilizing a pseudo-spectral method based on the reproducing kernel. Then, we provide two numerical examples to support the accuracy and efficiency of our proposed method. Finally, we apply numerical experiments to calculate the quality of our approximation by employing discrete error norms.

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Numerical investigation for Caputo-Fabrizio fractional Riccati and Bernoulli equations using iterative reproducing kernel method

Cited by 54 publications

References 45 publications

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

The Fractional Investigation of Some Nonlinear Partial Differential Equations by Using an Efficient Procedure

On a Class of Partial Differential Equations and Their Solution via Local Fractional Integrals and Derivatives

A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation

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