Numerical Solutions of Fractional Differential Equations by Using Laplace Transformation Method and Quadrature Rule

Fractal and Fractional

Mehdi Mesrizadeh¹  Carlo Cattani²  Samaneh Soradi-Zeid³ 

[1] Department of Mathematics, Kharazmi University, Karaj 14911-15719, Iran;Engineering School, DEIM, Tuscia University, 01100 Viterbo, Italy;Faculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan 98155-987, Iran;

关键词: fractional differential equation;    Laplace transform method;    time discretization;    quadrature rule;   

DOI  :  10.3390/fractalfract5030111

来源: DOAJ

【 摘 要 】

This paper introduces an efficient numerical scheme for solving a significant class of fractional differential equations. The major contributions made in this paper apply a direct approach based on a combination of time discretization and the Laplace transform method to transcribe the fractional differential problem under study into a dynamic linear equations system. The resulting problem is then solved by employing the numerical method of the quadrature rule, which is also a well-developed numerical method. The present numerical scheme, which is based on the numerical inversion of Laplace transform and equal-width quadrature rule is robust and efficient. Some numerical experiments are carried out to evaluate the performance and effectiveness of the suggested framework.

【 授权许可】

Unknown