Analysis of a System for Linear Fractional Differential Equations

Abstract

The main purpose of this paper is to obtain the unique solution of the constant coefficient homogeneous linear fractional differential equations Dt0qX(t)=PX(t),X(a)=B and the constant coefficient nonhomogeneous linear fractional differential equations Dt0qX(t)=PX(t)+D,X(a)=B if P is a diagonal matrix and X(t)∈C1-q[t0,T]×C1-q[t0,T]×⋯×C1-q[t0,T] and prove the existence and uniqueness of these two kinds of equations for any P∈L(Rm) and X(t)∈C1-q[t0,T]×C1-q[t0,T]×⋯×C1-q[t0,T]. Then we give two examples to demonstrate the main results.