Numerical Investigations of Fractional Complex Coupled Maccari and Cahn-Hilliard Equations Using Controlled Picard Iteration with ρ-Laplace Transform

This article presents a semi-analytical approach to address two nonlinear evolution equations: the fractional complex coupled Maccari system and the fractional Cahn-Hilliard equation. These mathematical models encapsulate essential concepts such as non-locality and memory, making them applicable in signal and image processing. The proposed method utilizes the controlled Picard framework combined with theρ-Laplace transform. The recommended approach eliminates the necessity for traditional techniques, such as Lagrange multipliers and Adomian expansions, by integrating the controlled Picard method with theρ-Laplace transformation. Additionally, a minimal parameter, ¯h, has been introduced to improve the convergence of the system under investigation. The results have been validated against exact solutions, and absolute error analyses support the accuracy of the proposed approach. The article includes 2D and 3D plots to illustrate how results vary with different parameters. In conclusion, this paper demonstrates that our method is explicit and efficiently executable.OPEN ACCESS Received: 25/03/2025 Accepted: 07/05/2025 Published: 30/05/2025