The Stochastic Linear Theta Method of McKean‐Vlasov Fractional Stochastic Differential Equations Driven by Time‐Changed Brownian Motions

This paper investigates a class of time‐changed McKean–Vlasov fractional stochastic differential equations. The presence of fractional singular kernels invalidates conventional analytical tools, such as the time‐changed Gronwall lemma. To overcome this difficulty, we establish an extended version of the time‐changed Gronwall lemma. Based on this new Gronwall lemma, we prove the existence and uniqueness of strong solutions for the considered equations. Furthermore, strong convergence and convergence rate in finite time of the stochastic linear theta method on the particle system are discussed. Two numerical examples are provided to illustrate the theoretical results.