Analysis of a system of fractional differential equations. (English) Zbl 1058.34002

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.


34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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