Abstract
We prove a maximal regularity result for abstract linear evolution autonomous equations with a fractional time derivative in the sense of Caputo. We employ it to show theorem of existence and uniqueness of local solutions for fully nonlinear equations and a theorem of existence of a stable manifold which is analogous to well known results in the case of a derivative of order one. We conclude with some examples and applications to mixed Cauchy-Dirichlet and Cauchy-Neumann problems.
Citation
Davide Guidetti. "On fully nonlinear equations with fractional time derivative: local existence and uniqueness, stable manifold." Adv. Differential Equations 29 (1/2) 69 - 110, January/Febraury 2024. https://doi.org/10.57262/ade029-0102-69
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