NUMERICAL SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS USING MODIFIED LAPLACE DECOMPOSITION METHOD

Abstract

The current paper aims at the resolution of the fractional differential equation numerically by the application of the Modified Laplace Decomposition Method (MLDM). The use of fractional differential equations in the modelling of complex systems with memory and hereditary behaviour is important in many areas of science and engineering. Nonetheless, this still makes these equations difficult to solve analytically since they are nonlocal.

The current study seeks to create an effective numerical method that uses a combination of the Laplace transform and the decomposition method to enhance the accuracy and rate of convergence of solutions. The process includes the conversion of the fractional differential equation into the Laplace domain, and then a series of solution decomposition. To test the performance of the proposed method, the proposed method is applied to various kinds of fractional equations.

The findings indicate that MLDM has high accuracy solutions with less computation complexity. The numerical analysis shows that the method is fast convergent and can give reliable results in comparison to the existing methods. The results also indicate that the MLDM is able to deal with nonlinear fractional equations without the need to discretize or approximate the derivatives.

To sum up, the Modified Laplace Decomposition Method is a powerful and effective mathematical instrument of numerical analysis of the fractional differential equations. It has great benefits in regards to simplicity, accuracy and computing efficiency. The research claims that MLDM can be extensively utilized in multiple fields of science where it is necessary to do fractional modeling