The field of fractional differential equations is moving towards the development of more efficient and accurate numerical methods for solving these complex equations. Researchers are exploring new approaches to approximate power-law kernels and improve the computational feasibility of existing methods. The use of exponential sum approximations and local domain boundary element methods are showing promising results. Noteworthy papers include:

• One paper presents a comprehensive framework for approximating the weakly singular power-law kernel using a finite sum of exponentials, which can be used to solve fractional differential equations with high accuracy.
• Another paper proposes an extension of the local domain boundary element method for solving nonlinear time fractional Fisher-KPP problems, which can handle two-dimensional problems with different definitions of the fractional derivative.