On time fractional pseudo-parabolic equations with nonlocal integral conditions

<p style='text-indent:20px;'>In this paper, we study the nonlocal problem for pseudo-parabolic equation with time and space fractional derivatives. The derivative is of Caputo type order <inline-formula><tex-math id="M1">\begin{document}$ \sigma,\; \; 0<\sigma<1 $\end{document}</tex-math></inline-formula> id="M2">\begin{document}$ \alpha,\beta >0 $\end{document}</tex-math></inline-formula>. In first part, obtain some results existence uniqueness our suitably chosen id="M3">\begin{document}$ \alpha, \beta technique uses a Sobolev embedding based on constructing Mittag-Leffler operator. second give ill-posedness regularized solution. An error estimate in id="M4">\begin{document}$ L^p between solution sought obtained.</p>