LAUSR

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 ρ α n → ρ α in an appropriate sense as α n → 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.