This paper investigates two different Leslie matrix solutions for the reduced biquaternion matrix equation \(AXB+CXD=E\) . Through the permutation matrices, the complex decomposition of reduced biquaternion matrices, and the Kronecker product, by leveraging the specific attributes of Leslie matrices, we transform the constrained reduced biquaternion matrix equation into an unconstrained form. Consequently, we derive the necessary and sufficient conditions for the existence of solutions in the form of Leslie matrices to the reduced biquaternion matrix equation \(AXB+CXD=E\) and provide a general expression for such solutions. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed algorithm.
