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 unique-ness 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 exam-ples and applications to mixed Cauchy-Dirichlet and Cauchy-Neumann problems.

ON FULLY NONLINEAR EQUATIONS WITH FRACTIONAL TIME DERIVATIVE: LOCAL EXISTENCE AND UNIQUENESS, STABLE MANIFOLD / Guidetti Davide. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 29:1-2(2024), pp. 69-110. [10.57262/ade029-0102-69]

ON FULLY NONLINEAR EQUATIONS WITH FRACTIONAL TIME DERIVATIVE: LOCAL EXISTENCE AND UNIQUENESS, STABLE MANIFOLD

Guidetti D.
Investigation
2024

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 unique-ness 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 exam-ples and applications to mixed Cauchy-Dirichlet and Cauchy-Neumann problems.
2024
ON FULLY NONLINEAR EQUATIONS WITH FRACTIONAL TIME DERIVATIVE: LOCAL EXISTENCE AND UNIQUENESS, STABLE MANIFOLD / Guidetti Davide. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 29:1-2(2024), pp. 69-110. [10.57262/ade029-0102-69]
Guidetti Davide
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/959497
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