On the Summability of Formal Solutions of Linear Partial Differential Equations
Journal of Dynamical and Control Systems
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Summability and fractional linear partial differential equations
Journal of Dynamical and Control Systems
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We consider the Cauchy problem for a general inhomogeneous linear partial differential equation with constant coefficients in two complex variables. We obtain necessary and sufficient conditions for the multisummability of formal solutions in terms of analytic continuation properties and growth estimates of some functions connected with the inhomogeneity. The results are presented in the general framework of 1/p-fractional equations.