Weak solutions for time-fractional evolution equations in Hilbert spaces

Paola Loreti; Daniela Sforza

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arXiv · 2106.07416

Weak solutions for time-fractional evolution equations in Hilbert spaces

Paola Loreti·Daniela Sforza

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Abstract

We introduce a notion of weak solution for abstract fractional differential equations, motivated by the definition of Caputo derivative. We prove existence results for weak and strong solutions. We also give two examples as application of our results: time-fractional wave equations and time-fractional Petrovsky systems.

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Paola Loreti, Daniela Sforza. 2021-06-14. Weak solutions for time-fractional evolution equations in Hilbert spaces. https://arxiv.org/abs/2106.07416

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