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Existence for a class of time-fractional evolutionary equations with applications involving weakly continuous operator

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Abstract

The aim of this paper is to deal with a new class of fractional evolutionary equations involving the time-fractional order integral and nonlinear weakly continuous operators. Exploiting the Rothe method and using a surjectivity result for weakly continuous operators, the solvability for the problem is established. The result is applied to prove the existence of solutions to time-fractional nonstationary incompressible Navier–Stokes equation and Navier–Stokes–Voigt equation.

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Acknowledgements

The author thanks the National Natural Science Foundation of China (No. 12201137), the Special Fund for Science and Technological Bases and Talents of Guangxi (No. GUIKE AD21220103) and the Start-up Project of Scientific Research on Introducing talents at school level in Guangxi Minzu University (No. 2019KJQD04).

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  1. College of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, 530006, People’s Republic of China

    Biao Zeng

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  1. Biao Zeng
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Zeng, B. Existence for a class of time-fractional evolutionary equations with applications involving weakly continuous operator. Fract Calc Appl Anal 26, 172–192 (2023). https://doi.org/10.1007/s13540-022-00125-0

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  • DOI: https://doi.org/10.1007/s13540-022-00125-0

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