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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.

34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
26A33Fractional derivatives and integrals (real functions)
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
Full Text: DOI
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