Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Fractional Evolution Differential Equations with Neutral Time Delay

In this paper, we demonstrate that neutral fractional evolution equations with finite delay possess a stable mild solution. Our model incorporates a mixed fractional derivative that combines the Riemann-Liouville and Caputo fractional derivatives with orders 0<alpha<1 and 1= Cb for b is an element of V. These inequalities are obtained by "scalarizing" X >= Cb via cone duality and then by minimizing the classical univariate Cantelli's bound over the scalarized inequalities. Three diverse applications to random matrices, tails of linear images of random vectors, and network homophily are also given.