Stability of a class of problems for time-space fractional pseudo-parabolic equation with datum measured at terminal time

Abstract

We consider terminal value problems for time-space fractional pseudo-parabolic equation subjected to a final/terminal value condition. In fact, fractional orders α,s are not exactly known in modeling. These are determined experimentally. The main purpose is to investigate the continuity of the solution with respect to the fractional order α∈(0,1), which accordingly answer the question: does ραn→ρα in an appropriate sense as αn→α? Firstly, a formulation for integral solutions has been established, which based on Laplace transform and spectral expansion of the Mittag-Leffler operators. Then, the desired continuity will be obtained by making use of resolvent representations of the Mittag-Leffler operators on Hankel's contour. Finally, we present some numerical examples to illustrate the proposed theory.