Continuity Result on the Order of a Nonlinear Fractional Pseudo-Parabolic Equation with Caputo Derivative

Abstract

In this paper, we consider a problem of continuity fractional-order for pseudo-parabolic equations with the fractional derivative of Caputo. Here, we investigate the stability of the problem with respect to derivative parameters and initial data. We also show that uω′→uω in an appropriate sense as ω′→ω, where ω is the fractional order. Moreover, to test the continuity fractional-order, we present several numerical examples to illustrate this property.

Keywords

• caputo derivative
• pseudo-parabolic equation
• well-posedness
• regularity estimates