This paper addresses a Cauchy problem for the following nonlinear time-fractional advection-dispersion equation \(\begin{aligned}_{0}D_{t}^{\alpha }u(x,t)+b{u_{x}}(x,t)-a{u_{xx}}(x,t)=S(x,t,u(x,t)), \quad x\in \left( 0,1\right) , t>0, \end{aligned}\) where \(_{0}D_{t}^{\alpha }\) denotes the Caputo fractional derivative of order \(\alpha \in \left( 0,1\right] \) , \(a,b>0\) , and S represents a nonlinear source function. The problem is severely ill-posed in the Hadamard sense due to a lack of stability in its solution. To overcome this difficulty, we construct a regularized solution using the modified quasi-boundary value method and propose a rule for selecting the regularization parameter. Under appropriate assumptions on the smoothness of the exact solution, we prove the convergence of the regularized solution and derive an explicit convergence rate.
