Pell polynomial solution of the fractional differential equations in the Caputo–Fabrizio sense

Abstract

In this paper, linear differential equations involving fractional and integer order derivatives are considered. Here fractional derivatives are defined in the Caputo–Fabrizio sense. A solution in the form of the truncated Pell series of the fractional differential equation is investigated. Firstly, the truncated Pell series solution is substituted into the fractional differential equation. Then, the collocation process leads to a system of linear equations. Finally, the unknown coefficients of the truncated Pell series are obtained by solving the linear system. The error and convergence analysis of the method is also presented. Additionally, the accuracy of the method is shown by numerical examples.