A q-homotopy analysis transformation method for solving (2 + 1)-dimensional coupled fractional nonlinear Schrödinger equations

The Schrödinger equation and its variants have wide-ranging applications in physics, and proposed here is a hybrid algorithm for solving (2+1)-dimensional coupled fractional nonlinear Schrödinger equations. The algorithm uses the [Formula: see text]-homotopy analysis method combined with Laplace transformation to obtain approximate solutions, and their existence and uniqueness are established using fixed-point theory. Numerical simulations confirm the effectiveness of the algorithm, showing that its approximate solutions are highly accurate with low computational complexity. This approach offers rapidly converging series solutions for various partial differential equations.