Fractional in time diffusion-wave equation and its numerical approximation

Delić, Aleksandra

doi:10.2298/fil1605375d

Cited by 6 publications

(2 citation statements)

References 8 publications

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“…A numerical algorithm based on Chebyshev wavelets was formulated by Zhou and Xu [24] to obtain the approximate solution for timefractional DWE. Numerous researchers have developed various methods for solving a time-fractional DWE; see [14,[25][26][27]. Recently, Kanwal et al [28] presented a Ritz-Galerkin method together with two-dimensional Genocchi polynomials to establish the numerical solutions of a time-fractional DWE and a time-fractional Klein-Gordon equation.…”

Section: Introductionmentioning

confidence: 99%

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

et al. 2019

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In this study, we have proposed an efficient numerical algorithm based on third degree modified extended B-spline (EBS) functions for solving time-fractional diffusion wave equation with reaction and damping terms. The Caputo time-fractional derivative has been approximated by means of usual finite difference scheme and the modified EBS functions are used for spatial discretization. The stability analysis and derivation of theoretical convergence validates the authenticity and effectiveness of the proposed algorithm. The numerical experiments show that the computational outcomes are in line with the theoretical expectations. Moreover, the numerical results are proved to be better than other methods on the topic.

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Section: Introductionmentioning

confidence: 99%

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

et al. 2019

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“…In addition, there are many other investigations for fractional heat equations; some numerical studies exist as well. Reference [34] investigated a numerical computation for the wave diffusion problem in fractional context. Reference [35] illustrated the numerical technique for the diffusion problem with fractional order derivative.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

Yavuz

Sene

2020

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This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physical results in the analysis and investigations. In this work, both the ρ-Laplace homotopy transform method (ρ-LHTM) and the heat balance integral method (HBIM) are successfully combined to solve the fractional incompressible second-grade fluid differential equations. Numerical simulations and their physical interpretations of the mentioned incompressible second-grade fluid model are ensured to illustrate the main findings. It is also proposed that one can recognize the differences in physical analysis of diffusions such as ballistic diffusion, super diffusion, and subdiffusion cases by considering the impact of the orders ρ and φ.

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Stability and numerical analysis of fractional BBM-Burger equation and fractional diffusion-wave equation with Caputo derivative

Mohan,

Prakash

2023

Opt Quant Electron

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Fractional in time diffusion-wave equation and its numerical approximation

Cited by 6 publications

References 8 publications

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms

Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

Stability and numerical analysis of fractional BBM-Burger equation and fractional diffusion-wave equation with Caputo derivative

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