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<p>The universal predictor–corrector method was developed and used for providing numerical approximate solutions to initial value problems involving generalized Caputo-type fractional derivatives. This numerical algorithm, which can be treated as an extension of the Adams–Bashforth–Moulton method, is universal in the sense that it deals with many Caputo-type mathematical models. This study is concerned, mainly, with error analysis of this new algorithm. Error bounds of the algorithm with non-uniform meshes are estimated. Accordingly, the order of convergence is provided. Some numerical experiments are discussed to confirm the theoretical results and to highlight the applicability, efficiency and accuracy of the studied algorithm.</p>

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Error analysis of the universal predictor–corrector algorithm for generalized fractional differential equations

  • 期刊论文

  • 发表日期：

    2025年2月10日

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  • Zaid Odibat

摘要

The universal predictor–corrector method was developed and used for providing numerical approximate solutions to initial value problems involving generalized Caputo-type fractional derivatives. This numerical algorithm, which can be treated as an extension of the Adams–Bashforth–Moulton method, is universal in the sense that it deals with many Caputo-type mathematical models. This study is concerned, mainly, with error analysis of this new algorithm. Error bounds of the algorithm with non-uniform meshes are estimated. Accordingly, the order of convergence is provided. Some numerical experiments are discussed to confirm the theoretical results and to highlight the applicability, efficiency and accuracy of the studied algorithm.