Theory analysis of left-handed Grünwald-Letnikov formula with \(0 < \alpha < 1\) to detect and locate singularities (Q1722211)

Summary: We study fractional-order derivatives of left-handed Grünwald-Letnikov formula with \(0 < \alpha < 1\) to detect and locate singularities in theory. The widely used four types of ideal singularities are analyzed by deducing their fractional derivative formula. The local extrema of fractional derivatives are used to locate the singularities. Theory analysis indicates that fractional-order derivatives of left-handed Grünwald-Letnikov formula with \(0 < \alpha < 1\) can detect and locate four types of ideal singularities correctly, which shows better performance than classical 1-order derivatives in theory.