Fractional Burgers Equations with Mixed Derivatives

Abstract

This paper studies a nonlinear fractional Burgers equation involving an Atangana–Baleanu time derivative and a Caputo space derivative. We establish existence and uniqueness results under suitable assumptions and formulate a Laplace variational iteration scheme for constructing approximate solutions. The convergence of the iterative procedure is analyzed under explicit conditions. An illustrative example is presented to examine the influence of the fractional order on the solution behavior and to recover the corresponding classical Burgers model as the fractional order approaches one.