This paper investigates an inverse problem for fractional Rayleigh‐Stokes equations with nonlinear source. The fractional derivative in time is taken in the sense of Riemann‐Liouville. The proposed problem has many applications in some non‐Newtonian fluids. We obtain some results on the existence and regularity of mild solutions.
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.
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