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On time fractional Partial Differential equations and Their Solution by Certain Formable Transform Decomposition Method

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Computer Modeling in Engineering & Sciences 2023年第9期136卷 3121-3139页

作者： Rania Saadeh Ahmad Qazza Aliaa Burqan Shrideh Al-Omari Department of Mathematics Zarqa UniversityZarqa13110Jordan Department of Mathematics Faculty of ScienceAl-Balqa Applied UniversityAmman11134Jordan

This paper aims to investigate a new efficient method for solving time fractional partial differential *** this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition ***,certain accurate solutions for time-fractional partial differential equations have been *** under concern demandsmore simple calculations and fewer efforts compared to the ***,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential ***,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing ***,the formable transform decomposition method has been employed for finding a series solution to a time-fractional klein-gordon *** and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.

关键词： Caputo derivative fractional differential equations formable transform time-fractional klein-gordon equation decomposition method

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Lattice Boltzmann Model for time-fractional NonlinearWave equations

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Advances in Applied Mathematics and Mechanics 2022年第4期14卷 914-935页

作者： Yibo Wang Rui Du Zhenhua Chai School of Mathematics Southeast UniversityNanjingJiangsu 210089China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhanHubei 430074China

In this paper,a lattice Boltzmann model with BGK operator(LBGK)for solving time-fractional nonlinear wave equations in Caputo sense is ***,the Caputo fractional derivative is approximated using the fast evolution algorithm based on the sum-of-exponentials *** the target equation is transformed into an approximate form,and for which a LBGK model is *** the Chapman-Enskog analysis,the macroscopic equation can be recovered from the present LBGK *** addition,the proposed model can be extended to solve the time-fractional klein-gordon equation and the time-fractional Sine-gordon ***,several numerical examples are performed to show the accuracy and efficiency of the present LBGK *** the numerical results,the present model has a second-order accuracy in space.

关键词： Lattice Boltzmann method time-fractional wave equation time-fractional klein-gordon equation time-fractional Sine-gordon equation

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