Defining Function Dependence of Riemann–Liouville Plastic Flow on a Common Convex Yield Surface

A fractional flow direction need not be determined by its yield boundary. We study a componentwise left Riemann–Liouville operator with fixed coordinates, scales, terminals and internal variables. Proposition 2 constructs two globally strictly convex polynomial functions. They define the same closed ellipse and have identical boundary derivatives through any prescribed finite order. Their normalized fractional directions nevertheless differ for every order between zero and one. A half-order circle example gives an exact separation of 30.008768 degrees. Thus, neither strict convexity nor finite boundary data restore representation invariance. Polynomial identities, adaptive quadrature and independent Grünwald–Letnikov refinement verify the construction. A published modified Cam-clay surface provides a further operator benchmark. A coupled AJOP-T diagnostic and Lode scans then illustrate possible mechanical consequences under stated admissibility conditions. The main result identifies constitutive information that cannot be recovered from finite boundary data alone. These synthetic tests verify the equations and implementation. They do not calibrate or validate a material model.