Solving fractional partial differential equations via a new scheme

Qazza, Ahmad; Saadeh, Rania; Salah, Emad

doi:10.3934/math.2023267

Cited by 16 publications

(8 citation statements)

References 36 publications

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“…Using the suggested approach, we were able to effectively generate accurate approximation solutions and illustrate the dynamical behaviors of the systems under discussion. This research was carried out in the hope that it will be a useful resource for future applications and explorations of generalized Caputo fractional problems, and to investigate new methods such as those in [37][38][39][40][41].…”

Section: Discussionmentioning

confidence: 99%

A Numerical Solution of Generalized Caputo Fractional Initial Value Problems

et al. 2023

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In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM method was utilized to establish approximate series solutions. The presented technique is considered to be an extension to the original Adams–Bashforth–Moulton approach. Numerical simulations and figures are presented and discussed, in order to show the efficiency of the proposed method. In the future, we anticipate that the provided generalized Caputo fractional derivative and the suggested method will be utilized to create and simulate a wide variety of generalized Caputo-type fractional models. We have included examples to demonstrate the accuracy of the present method.

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Section: Discussionmentioning

confidence: 99%

A Numerical Solution of Generalized Caputo Fractional Initial Value Problems

et al. 2023

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“…Te study of the SIR model was frst introduced in 2009 by Ahmet and Cherruault [19], then in 2011 they present new research on analytical solutions of some related models. After that, many authors have investigated the susceptible-infected recovered models of integer fractional orders [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

On the Analytical Solution of Fractional SIR Epidemic Model

Qazza

Saadeh

2023

Applied Computational Intelligence and Soft Computing

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This article presents the solution of the fractional SIR epidemic model using the Laplace residual power series method. We introduce the fractional SIR model in the sense of Caputo’s derivative; it is presented by three fractional differential equations, in which the third one depends on the first coupled equations. The Laplace residual power series method (LRPSM) is implemented in this research to solve the proposed model, in which we present the solution in a form of convergent series expansion that converges rapidly to the exact one. We analyze the results and compare the obtained approximate solutions to those obtained from other methods. Figures and tables are illustrated to show the efficiency of the LRPSM in handling the proposed SIR model.

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“…Tere are various analytical and numerical methods available for handling various forms of ffth-order KdV-type equations in the literature. Some of them are the Adomian decomposition technique [35], modifed Adomian decomposition method [36], Laplace decomposition approach [37], diferential transform technique [38,39], Hirota's bilinear techniques [40], inverse scattering algorithm [41], He's semiinverse scheme [42], extended Tanh method [43], homotopy analysis technique [14,44], fractional homotopy analysis transform algorithm [45], modifed homotopy perturbation technique [46], variational iteration technique [47], homotopy perturbation method [48,49], homotopy perturbation transform method [50], hyperbolic and exponential ansatz methods [51], multiple exp-function method [52], and others [53][54][55]. Moreover, many methods are available to solve the fractional-order KdV equations.…”

Section: Introductionmentioning

confidence: 99%

A New Computational Technique for Analytic Treatment of Time-Fractional Nonlinear Equations Arising in Magneto-Acoustic Waves

Prakasha

Saadeh

Kachhia

et al. 2023

Mathematical Problems in Engineering

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This paper presents the study of time-fractional nonlinear fifth-order Korteweg–de Vries equations by utilizing an adequate novel technique, namely, the q-homotopy analysis transform method. The fifth-order Korteweg–de Vries equation has got its importance in the study of magneto-sound propagation in plasma, capillary gravity water waves, and the motion of long waves under the influence of gravity in shallow water. To justify the effectiveness and pertinence of the contemplated technique, we take a look at three examples of the time-fractional fifth-order Korteweg–de Vries equations. The q-homotopy analysis transform method offers us to modulate the range of convergence of the series solution using ℏ, called the auxiliary parameter or convergence control parameter. The study of the fractional behaviour of the considered equations expresses the originality of the presented work. There is a visible variation in the obtained solutions for different fractional orders and which can lead to different consequences for future work. As a future research direction, readers can use the hybrid methodologies merging with our projected scheme to achieve better consequences. Additionally, to validate the precision and reliability of the proposed method, we organized suitable numerical simulations. The obtained findings show that the proposed method is very gratifying and examines the complex nonlinear challenges that arise in science and innovation.

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Solving fractional partial differential equations via a new scheme

Cited by 16 publications

References 36 publications

A Numerical Solution of Generalized Caputo Fractional Initial Value Problems

A Numerical Solution of Generalized Caputo Fractional Initial Value Problems

On the Analytical Solution of Fractional SIR Epidemic Model

A New Computational Technique for Analytic Treatment of Time-Fractional Nonlinear Equations Arising in Magneto-Acoustic Waves

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