An Efficient Exponential Sum Approximation of Power-Law Kernels for Solving Fractional Differential Equation

2025/08/27 by Renu Chaudhary, Chaudhary, Renu, Kai Diethelm +4
Computer Science · Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2508.20311

openalex publication_date 2025/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we present a comprehensive framework for approximating the weakly singular power-law kernel t^α-1 of fractional integral and differential operators, where α∈ (0,1) and t ∈ [δ,T] with 0<δ

Citations

• Novel Variants of Diffusive Representation of Fractional Integrals: Construction and Numerical Computation
• Revisiting Diffusive Representations for Enhanced Numerical Approximation of Fractional Integrals
• Numerical Evaluation of Two and Three Parameter Mittag-Leffler Functions
• A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations
• Approximation by exponential sums revisited
• A Fast Time Stepping Method for Evaluating Fractional Integrals
• On approximation of functions by exponential sums

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