On backward fractional pseudo parabolic equation: Regularization by quasi-boundary value method, convergence rates

This paper is concerned with the backward problem of recovering initial value for a homogeneous time-space fractional pseudo parabolic differential equation. Since the problem is ill-posed, a version of modified quasi boundary value method is used as the method of regularization for obtaining stable approximations. Error analysis and parameter choice strategies are done for both a priori and a posteriori cases. It is shown that, the order of the convergence rate can exceed \(\frac{2}{3}.\) $\frac{2}{3}.$ Hence, the obtained rate improves upon the previously known rates of order \(\frac{2}{3}\) $\frac{2}{3}$ for the a priori case, and \(\frac{1}{2}\) $\frac{1}{2}$ for the a posteriori case for the considered problem.