A New and Elegant Approach for Solving $$\varvec{n \times n}$$ n × n -Order Linear Fractional Differential Equations

Abstract

The application of fractional differential equations (FDEs) in the fields of science and engineering are gradually increasing day by day during the last two decades. The solutions of linear systems of FDEs are of great importance. Several investigations are carried out on such systems using eigenvalue analysis or Laplace transform method. But both the methods have limitations, and as of now there are no methods for solving $$n \times n$$ -order linear FDEs. In the present investigation, the issues of such difficulties are addressed, and the exact solutions of linear $$2 \times 2$$ -order linear FDEs are presented by Laplace transform. We are unable to provide the exact solutions of such system of order $$n \times n$$ by Laplace transform. To overcome this, we provide a new and elegant approach to find the approximate solutions of $$n \times n$$ -order linear FDEs with the help of residual power series (RPS) method. The results thus obtained are verified by providing numerous examples.