Fractional differentiation method: Some applications to the theory of subdiffusion-controlled reactions

Area of Science:

• * Mathematical Physics
• * Physical Chemistry
• * Chemical Physics

Background:

• * Anomalous diffusion and reaction-diffusion systems are crucial in various scientific fields.
• * Traditional methods for solving these problems can be computationally intensive.
• * Fractional calculus offers a powerful alternative for modeling complex diffusion dynamics.

Purpose of the Study:

• * To demonstrate the utility of the fractional differentiation method for anomalous diffusion trapping problems.
• * To evaluate reaction rate coefficients for subdiffusion-controlled reactions.
• * To provide a method for solving diffusion equations with fractional time derivatives.

Main Methods:

• * Application of the fractional differentiation method.
• * Evaluation of reaction rate coefficients using a factorization procedure.
• * Analysis of diffusion equations with half-order time derivatives (Riemann-Liouville sense).

Main Results:

• * The fractional differentiation method effectively determines reaction rate coefficients.
• * This method bypasses the need for preliminary solutions to complex diffusion problems.
• * It provides a direct route to obtaining coefficients for subdiffusion and damping terms.

Conclusions:

• * The fractional differentiation method offers a significant advancement in solving reaction-diffusion problems.
• * It provides a computationally efficient and direct approach for evaluating reaction rate coefficients.
• * The method's mathematical background is detailed for broad applicability to time-fractional diffusion problems.