Global well-posedness for fractional Sobolev-Galpern type equations

<p style='text-indent:20px;'>This article is a comparative study on an initial-boundary value problem for class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called Sobolev-Galpern type equations. The purpose this work to reveal influence degree source nonlinearity well-posedness solution. By considering four different types nonlinearities, we derive global mild solutions corresponding cases nonlinear terms. For advection function case, apply nontrivial limit technique singular integral and some appropriate choices weighted Banach space prove existence result. gradient as local Lipschitzian, use Cauchy sequence show that solution either exists globally in time or blows up at finite time. polynomial form nonlinearity, by assuming smallness initial data well-posed results. And case exponential two-dimensional space, additionally using Orlicz space.</p>