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

Area of Science:

• Mathematical Physics
• Nonlinear Dynamics
• Fractional Calculus

Background:

• Fractional reaction-diffusion systems model complex phenomena with memory effects.
• Classical calculus methods may not fully capture nonlocal dynamics inherent in these systems.
• The conformable fractional operator offers a simplified approach to fractional modeling.

Purpose of the Study:

• To analytically investigate fractional reaction-diffusion systems using the conformable fractional operator.
• To reduce fractional partial differential equations to ordinary differential forms for solution derivation.
• To validate the proposed framework by comparing solutions with the Homotopy Perturbation Method (HPM).

Main Methods:

• Application of the conformable fractional operator.
• Utilizing similarity transformations to simplify governing equations.
• Derivation of analytical and approximate solutions.
• Comparison with solutions obtained via the Homotopy Perturbation Method (HPM).

Main Results:

• Analytical and approximate solutions were derived for fractional reaction-diffusion systems.
• The conformable fractional operator proved efficient and accurate for nonlinear systems.
• A reduction in fractional order was shown to enhance nonlocality and slow diffusion processes.
• The study successfully bridged classical and fractional modeling approaches.

Conclusions:

• The conformable fractional operator is a powerful tool for modeling fractional-order processes with memory effects.
• This framework provides a robust theoretical foundation for applications in mathematical biology, chemical physics, and engineering.
• The findings deepen the understanding of fractional transport phenomena and nonlocal dynamics.