Amyloid fibrils are important biological structures associated with devastating human diseases such as Alzheimer disease, as well as have vital biological functions such as adhesion and biofilm formation. The division of amyloid protein fibrils is required for the propagation of the amyloid state and is an important contributor to their stability, pathogenicity, and normal function. We apply asymptotic results on the fragmentation equation to develop an inverse problem approach, allowing us to compare the division stability of amyloid fibrils and estimate their division features (fragmentation rate and kernel).