What question did this study set out to answer?

This work aims to review and compare numerical frameworks for solving high-order ordinary and fractional differential equations.

Advanced Spectral-Operational Frameworks for Fractional and Integer-Order Differential Equations: A Methodological Review

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Methodological review demonstrates advanced frameworks for differential equations, suggesting enhanced accuracy in solutions.

This work aims to review and compare numerical frameworks for solving high-order ordinary and fractional differential equations.
Comprehensive analysis of frameworks for initial and boundary value problems involving various types of differential equations.
Construction of operational matrices for ordinary, fractional, and variable-order derivatives using generalized shifted Jacobi polynomials.
Application of spectral collocation methods to transform differential equations into solvable algebraic systems.
The proposed methodologies exhibit significant accuracy and robustness in solving complex fractional differential equations.
Compared to existing methods, the new frameworks offer better accuracy-cost ratios.
Numerical examples validate the effectiveness of these operational frameworks.

H. M. Ahmed (2026) studied this question.

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