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

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.

Automated summary

This paper introduces an efficient numerical scheme for solving a significant class of fractional differential equations using a combination of Laplace transform and trapezoidal rule methods. The scheme, based on numerical inversion and equal-width trapezoidal rule, is robust and efficient. Numerical experiments are conducted to evaluate the performance and effectiveness of the suggested framework.