Analysis of a system of fractional differential equations (Q1827105)

The authors investigate the system of fractional differential equations \[ D^\alpha [\overline {x}(t)- \overline {x}(0)]= A\overline {x}(t), \qquad \overline {x}(0)= \overline {x}_0, \quad 0< \alpha< 1, \] where \(D^\alpha\) denotes the Riemannian-Liouville derivative operator and \(A\) is a square matrix having real entries. They discuss the initial value problem for the nonautonomous nonlinear system \[ D^\alpha [\overline {x}(t)- \overline {x}(0)]= f(t,\overline {x}), \quad \overline {x}(0)= \overline {x}_0. \qquad 0< \alpha< 1. \] The dependence of the solutions on the initial conditions is also studied.