Analytical solutions and dynamic behavior of conformable fractional reaction-diffusion systems

This study presents an analytical investigation of fractional reaction-diffusion systems within the framework of the conformable fractional operator. The conformable operator provides a simplified yet powerful mathematical tool for modeling fractional-order processes, preserving the essential properties of classical calculus while capturing memory and hereditary effects inherent in diffusion-reaction dynamics. By applying appropriate similarity transformations, the governing fractional partial differential equations are reduced to conformable ordinary differential forms, allowing the derivation of analytical and approximate solutions. To validate the reliability and accuracy of the proposed analytical framework, the obtained solutions are systematically compared with those derived from the Homotopy Perturbation Method (HPM). The influence of the fractional order and key physical parameters on wave propagation, concentration profiles, and diffusion behavior is thoroughly examined, showing that a reduction in fractional order enhances nonlocality and slows the diffusion process. The results confirm that the conformable fractional operator offers an efficient and accurate approach for describing nonlinear diffusion-reaction systems, effectively bridging classical and fractional models. This work deepens the understanding of fractional transport processes and provides a strong theoretical foundation for future applications in mathematical biology, chemical physics, and engineering systems governed by complex nonlocal dynamics.