August 15, 2025MathematicsOpen Access

A Spectral Approach to Variable-Order Fractional Differential Equations: Improved Operational Matrices for Fractional Jacobi Functions

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The proposed technique improves accuracy in solving variable-order fractional differential equations, particularly with initial conditions and numerical examples.
Generalized fractional Jacobi functions were introduced, which satisfy associated initial conditions while enhancing operational matrices for fractional derivatives.
Utilizing the spectral collocation method allows for the development of effective operational matrices, leading to efficient solutions in fractional calculus.
The error analysis ensures the validity of the algorithm, highlighting the feasibility of the procedure with successful numerical test examples.

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Implication

This method demonstrates improved computational accuracy for variable-order fractional differential equations, implying efficient problem-solving techniques.

Cite This Study

Ahmed et al. (2025) studied this question.

synapsesocial.com/papers/68a3656a0a429f797332b8b2 https://doi.org/10.3390/math13162544

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Implication

This method demonstrates improved computational accuracy for variable-order fractional differential equations, implying efficient problem-solving techniques.

A Spectral Approach to Variable-Order Fractional Differential Equations: Improved Operational Matrices for Fractional Jacobi Functions

Key Points

Discussion

Implication

Cite This Study

A Spectral Approach to Variable-Order Fractional Differential Equations: Improved Operational Matrices for Fractional Jacobi Functions

Key Points

Discussion

Implication

Cite This Study

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Also Consider