2020
DOI: 10.3390/math8111972
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A Meshless Method Based on the Laplace Transform for the 2D Multi-Term Time Fractional Partial Integro-Differential Equation

Abstract: In this article, we propose a localized transform based meshless method for approximating the solution of the 2D multi-term partial integro-differential equation involving the time fractional derivative in Caputo’s sense with a weakly singular kernel. The purpose of coupling the localized meshless method with the Laplace transform is to avoid the time stepping procedure by eliminating the time variable. Then, we utilize the local meshless method for spatial discretization. The solution of the original problem … Show more

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Cited by 12 publications
(5 citation statements)
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“…Other method are also available for the solving the problem for laplacian operator. A meshless method was explained by Kamran et al [26] which is based on laplace transform for the two dimensional multiple term time for fractional partial integral differential equations [26]. Same scenario with approximation of matrics and spectral analysis was done by Aceto, et al [27].…”
Section: Eigenvalues With Laplacian Operatormentioning
confidence: 99%
“…Other method are also available for the solving the problem for laplacian operator. A meshless method was explained by Kamran et al [26] which is based on laplace transform for the two dimensional multiple term time for fractional partial integral differential equations [26]. Same scenario with approximation of matrics and spectral analysis was done by Aceto, et al [27].…”
Section: Eigenvalues With Laplacian Operatormentioning
confidence: 99%
“…In [22], the collocation method combined with fractional Genocchi functions is used for the solution of variable-order FIDEs. In [23], the meshless method based on the Laplace transform is constructed for approximating the solution of the two-dimensional multi-term FIDEs. In [24], the finite element method is proposed to solve the two-dimensional weakly singular FIDEs.…”
Section: Introductionmentioning
confidence: 99%
“…Yang et al [38] employed the moving least squares approximation method for the numerical approximation of fractional diffusion wave equations. Other works on the applications of RBF-based local meshless methods can be found in the references (see [39][40][41][42] and the references therein).…”
Section: Introductionmentioning
confidence: 99%