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The aim is to review computational methods for fractional differential equations, focusing on numerical solvers and learning-based approaches.

A Critical Review of Computational Methods for Fractional Differential Equations: Bridging Classical Discretizations and Learning-Based Approximations

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This critical review analyzes numerical methods for fractional differential equations, highlighting classical and learning-based techniques.

The aim is to review computational methods for fractional differential equations, focusing on numerical solvers and learning-based approaches.
Collected classical discretization methods for fractional equations
Reviewed contemporary acceleration and optimization strategies
Examined various numerical techniques including finite differences and neural networks
Proposed a classification scheme for existing solvers based on discretization methods
Provided a comprehensive overview of state-of-the-art numerical solvers
Addressed scalability issues in variable order solvers
Unified treatment of deterministic and stochastic fractional cases
Proposed a classification scheme to help researchers avoid implementation challenges

Dozva et al. (2026) studied this question.

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This critical review analyzes numerical methods for fractional differential equations, highlighting classical and learning-based techniques.