## 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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### References:

 [1] Aliprantis, C.D.; Burkinshaw, O., Principles of real analysis, (1990), Academic Press New York · Zbl 0436.46009 [2] Delbosco, D.; Rodino, L., Existence and uniqueness for a nonlinear fractional differential equation, J. math. anal. appl., 204, 609-625, (1996) · Zbl 0881.34005 [3] Diethelm, K.; Ford, N.J., Analysis of fractional differential equations, J. math. anal. appl., 265, 229-248, (2002) · Zbl 1014.34003 [4] Hirsch, M.V.; Smale, S., Differential equations, dynamical systems and linear algebra, (1974), Academic Press New York · Zbl 0309.34001 [5] Luchko, Y.; Gorenflo, R., An operational method for solving fractional differential equations with the Caputo derivatives, Acta math. Vietnam., 24, 207-233, (1999) · Zbl 0931.44003 [6] Perko, L., Differential equations and dynamical systems, (1991), Springer-Verlag New York · Zbl 0717.34001 [7] Podlubny, I., Fractional differential equations, (1999), Academic Press New York · Zbl 0918.34010 [8] Precup, R., Methods in nonlinear integral equations, (2002), Kluwer Academic Dordrecht · Zbl 1060.65136 [9] Samko, S.; Kilbas, A.; Marichev, O., Fractional integrals and derivatives, (1993), Gordon and Breach Yverdon · Zbl 0818.26003
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