Existence and Decay of Mild Solutions for the Time‐Space Fractional Burgers Equations

This study investigates the Cauchy problem related to the time‐space fractional Burgers equation, expanding on the classical Burgers equation by substituting the standard integer‐order time derivative with the Caputo fractional‐order derivative and replacing the classic Laplacian with a fractional Laplacian. The research employs fractional heat kernel estimates and the Mittag–Leffler function to establish initial estimates for solution operators, focusing on both local and global mild solutions within Lebesgue spaces and their decay properties. The main proof leverages the fixed‐point theorem, offering new theoretical perspectives on fractional Burgers equations.