On the Existence and Uniqueness of the Solution of Linear Fractional Differential-Algebraic System

الملخص EN

The existence and uniqueness of the solution of a new kind of system—linear fractional differential-algebraic equations (LFDAE)—are investigated.

Fractional derivatives involved are under the Caputo definition.

By using the tool of matrix pair, the LFDAE in which coefficients matrices are both square matrices have unique solution under the condition that coefficients matrices make up a regular matrix pair.

With the help of equivalent transformation and Kronecker canonical form of the coefficients matrices, the sufficient condition for existence and uniqueness of the solution of the LFDAE in which coefficients matrices are both not square matrices is proposed later.

Two examples are given to justify the obtained theorems in the end.