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Cauchy-type problem for an abstract differential equation with fractional derivatives. (English. Russian original) Zbl 1086.34050
Math. Notes 77, No. 1, 26-38 (2005); translation from Mat. Zametki 77, No. 1, 28-41 (2005).
The author proves the uniform well-posedness of a Cauchy-type problem with two fractional derivatives and a bounded operator A. For an unbounded operator A, the author presents a test for the uniform well-posedness of the problem under consideration consistent with the test for the uniform well-posedness of the Cauchy problem for an equation of second order.

MSC:
34G10 Linear differential equations in abstract spaces
26A33 Fractional derivatives and integrals
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