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<p>This paper introduces a novel numerical approach for solving nonlinear fractional differential equations (FDEs) using the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Upsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Υ</mi> </math></EquationSource> </InlineEquation>-Caputo fractional derivative. By transforming the problem into a Volterra integral equation, we establish a solid framework for analyzing stability and convergence. We propose efficient numerical schemes based on uniform partitions, which avoid the need for variable transformations. To the best of our knowledge, this represents the first application of these schemes to FDEs. Extensive numerical tests validate the method’s accuracy, efficiency, and robustness, making it a valuable tool for solving nonlinear FDEs.</p>

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Accurate and Efficient Numerical Schemes for Nonlinear Fractional Differential Equations: Stability, Convergence, and Error Analysis

  • 期刊论文

  • 发表日期：

    2026年2月18日

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  • Sami Baroudi,
  • Naoufel Hatime,
  • Ali El Mfadel,
  • Abderrazak Kassidi,
  • M’hamed Elomari

摘要

This paper introduces a novel numerical approach for solving nonlinear fractional differential equations (FDEs) using the \(\Upsilon \) Υ -Caputo fractional derivative. By transforming the problem into a Volterra integral equation, we establish a solid framework for analyzing stability and convergence. We propose efficient numerical schemes based on uniform partitions, which avoid the need for variable transformations. To the best of our knowledge, this represents the first application of these schemes to FDEs. Extensive numerical tests validate the method’s accuracy, efficiency, and robustness, making it a valuable tool for solving nonlinear FDEs.