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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.

MSC:

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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