Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Journal of Dynamical and Control Systems
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We consider the Cauchy problem for Kowalevskaya-type fractional linear partial differential equations with constant coefficients in two complex variables. We show that the solutions can be analytically continued into certain sectors and have at most exponential growth there if and only if the Cauchy data have an appropriate property. Applying this result to the study of formal power series solutions of non-Kowalevskian linear partial differential equations, we obtain a characterization of Borel summable solutions in terms of analytic continuation property and growth estimations of the Cauchy data. We also obtain a similar result in the case of non-Kowalevskian fractional equations.