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On time fractional pseudo-parabolic equations with nonlocal integral conditions

  • * Corresponding author: Nguyen H. Tuan

    * Corresponding author: Nguyen H. Tuan
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  • In this paper, we study the nonlocal problem for pseudo-parabolic equation with time and space fractional derivatives. The time derivative is of Caputo type and of order $ \sigma,\; \; 0<\sigma<1 $ and the space fractional derivative is of order $ \alpha,\beta >0 $. In the first part, we obtain some results of the existence and uniqueness of our problem with suitably chosen $ \alpha, \beta $. The technique uses a Sobolev embedding and is based on constructing a Mittag-Leffler operator. In the second part, we give the ill-posedness of our problem and give a regularized solution. An error estimate in $ L^p $ between the regularized solution and the sought solution is obtained.

    Mathematics Subject Classification: 26A33, 35B65, 35R11.


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