Application of Jordan canonical form and symplectic matrix in fractional differential models

Abstract

Under consideration of this paper is the application of Jordan canonical form and symplectic matrix to two conformable fractional differential models. One is the new conformable fractional vector conduction equation which is reduced by using the Jordan canonical form of coefficient matrix and solved exactly, and the other is the new conformable fractional vector dynamical system with Hamilton matrix and symplectic matrix, which is derived by constructing the conformable fractional Euler-Lagrange equation and using fractional variational principle. It is shown that Jordan canonical form and symplectic matrix can be used to deal with some other conformable fractional differential systems in mathematical physics.