A numerical technique for solving fractional Benjamin–Bona–Mahony–Burgers equations with bibliometric analysis

Sabermahani, Sedigheh; Ordokhani, Yadollah

doi:10.1016/b978-0-32-390953-2.00013-x

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…Moreover, Burgers' equations and fractional Burgers' equations have been used to model heat conduction in fractal materials. The fractional derivative captures the non-local aspect of heat conduction, making it possible to investigate heat transport in fractal media or materials with memory effects [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

A Potent Collocation Approach Based on Shifted Gegenbauer Polynomials for Nonlinear Time Fractional Burgers’ Equations

Magdy,

Abd-Elhameed,

Youssri

et al. 2023

Contemp. Math.

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This paper presents a numerical strategy for solving the nonlinear time fractional Burgers's equation (TFBE) to obtain approximate solutions of TFBE. During this procedure, the collocation approach is used. The proposed numerical approximations are supposed to be a double sum of the products of two sets of basis functions. The two sets of polynomials are presented here: a modified set of shifted Gegenbauer polynomials and a shifted Gegenbauer polynomial set. Some specific integers and fractional derivatives are explicitly given as a combination of basis functions to apply the proposed collocation procedure. This method transforms the governing boundary-value problem into a set of nonlinear algebraic equations. Newton's approach can be used to solve the resulting nonlinear system. An analysis of the precision of the proposed method is provided. Various examples are presented and compared to some existing methods in the literature to prove the reliability of the suggested approach.

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Section: Introductionmentioning

confidence: 99%

A Potent Collocation Approach Based on Shifted Gegenbauer Polynomials for Nonlinear Time Fractional Burgers’ Equations

Magdy,

Abd-Elhameed,

Youssri

et al. 2023

Contemp. Math.

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New generalized Jacobi–Galerkin operational matrices of derivatives: an algorithm for solving the time-fractional coupled KdV equations

Ahmed

2024

Bound Value Probl

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The present paper investigates a new method for computationally solving the time-fractional coupled Korteweg–de Vries equations (TFCKdVEs) with initial boundary conditions (IBCs). The method utilizes a set of generalized shifted Jacobi polynomials (GSJPs) that adhere to the specified initial and boundary conditions (IBCs). Our approach involves constructing operational matrices (OMs) for both ordinary derivatives (ODs) and fractional derivatives (FDs) of the GSJPs we employ. We subsequently employ the collocation spectral method using these OMs. This method successfully converts the TFCKdVEs into a set of algebraic equations, greatly simplifying the task. In order to assess the efficiency and precision of the proposed numerical technique, we utilized it to solve two distinct numerical instances.

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A numerical technique for solving fractional Benjamin–Bona–Mahony–Burgers equations with bibliometric analysis

Cited by 2 publications

References 21 publications

A Potent Collocation Approach Based on Shifted Gegenbauer Polynomials for Nonlinear Time Fractional Burgers’ Equations

A Potent Collocation Approach Based on Shifted Gegenbauer Polynomials for Nonlinear Time Fractional Burgers’ Equations

New generalized Jacobi–Galerkin operational matrices of derivatives: an algorithm for solving the time-fractional coupled KdV equations

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