Laplace transform collocation and Daftar-Gejii-Jafaris method for fractional order time varying linear dynamical systems

Abstract

In this article, the fractional order time-varying linear dynamical system defined by Caputo derivative is investigated. Laplace transform collocation method (LTCM) and Daftar-Gejii-Jafaris method (DGJM) are used to find the approximation solution of this equation. Using the Laplace transform collocation method, a new form of trial function from the original equation is presented. The unknown coefficients in the trial functions are calculated by using collocation method. LTCM gives a good result for the numerical solution of this equation. Providing DGJM converges, it is shown that obtained approximate solution is effective which is close to the exact solution. Then, the exact solution is compared with these approximate solutions. The results showed that the methods are effective and useful. These methods produced better approximations than the ones produced with the standard weighted residual methods.