In this paper, a modified hybrid B-spline approximation based on spatial regulator tensor network (MHBA-SRTN) is proposed for solving the application and the feasibility problems of fractional calculus-based Burger equation. The main innovation points include: (1) a dual singular kernel based fractional derivative operator is employed on the Burger’s equation with external force term to analyze the solutions and properties under perturbation condition for further realism simulation; (2) a modified hybrid B-spline basis function and its corresponding topological tensor network structure are further proposed to solve the provided Burger’s equation with more favorable approximation accuracy and solution uniqueness; (3) the tensor network transformed the hybrid B-spline construction process into the tensor solving with the introduced spatially regulated tensor network decomposition for a more robust solution procedure; (4) an acceleration approach for decomposition process is introduced to significantly reduce its computational and storage complexity. Extensive experiments are also carried out to verify the performance of MHBA-SRTN.