Application of Laplace residual power series method for approximate solutions of fractional IVP’s

Abstract

In this study, different systems of linear and non-linear fractional initial value problems are solved analytically utilizing an attractive novel technique so-called the Laplace residual power series approach, and which is based on the coupling of the residual power series approach with the Laplace transform operator to generate analytical and approximate solutions in fast convergent series forms by using the concept of the limit with less time and effort compared with the residual power series technique. To confirm the simplicity, performance, and viability of the proposed technique, three problems are tested and simulated. Analysis of the obtained results reveals that the aforesaid technique is straightforward, accurate, and suitable to investigate the solutions of the non-linear physical and engineering problems.

Keywords

• Fractional initial value problems
• Caputo’s derivative operator
• Laplace residual power series
• Fractional power series