z-logo
open-access-imgOpen Access
On time fractional pseudo-parabolic equations with nonlocal integral conditions
Author(s) -
Nguyễn Anh Tuấn,
Donal O’Regan,
Dumitru Băleanu,
Nguyễn Huy Tuấn
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2020109
Subject(s) - mathematics , uniqueness , order (exchange) , sobolev space , fractional calculus , space (punctuation) , operator (biology) , mathematical analysis , linguistics , philosophy , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene
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 \begin{document}$ \sigma,\; \; 0<\sigma<1 $\end{document} and the space fractional derivative is of order \begin{document}$ \alpha,\beta >0 $\end{document} . In the first part, we obtain some results of the existence and uniqueness of our problem with suitably chosen \begin{document}$ \alpha, \beta $\end{document} . The technique uses a Sobolev embedding and is based on constructing a Mittag-Leffler operator. In the second part, we give the ill-posedness of our problem and give a regularized solution. An error estimate in \begin{document}$ L^p $\end{document} between the regularized solution and the sought solution is obtained.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.
Having issues? You can contact us here