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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 for ODE, existence, uniqueness, etc. of solutions 26A33 Fractional derivatives and integrals (real functions) 34A25 Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
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##### References:
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