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<p>In this study, we consider two classes of variable order fractional differential equations (VOFDEs) and pantograph VOFDEs. The current method incorporates Ritz and optimization techniques based on a set of wavelet functions. We use Mittag-Leffler wavelets to achieve this goal. We have developed an extra variable order (VO) Caputo pseudo-operational matrix and a pantograph operational matrix for Mittag-Leffler wavelets as new achievements. Using these matrices, along with Ritz and optimization methods, we determine an approximate solution for each of the considered problems. An estimate of errors is proposed, and numerical experiments are performed to demonstrate the performance and high accuracy of the current approach.</p>

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Ritz-Mittag-Leffler Wavelet Technique for Solving Variable Order Fractional Differential Equations

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • Arezoo Ghasempour,
  • Yadollah Ordokhani,
  • Sedigheh Sabermahani

摘要

In this study, we consider two classes of variable order fractional differential equations (VOFDEs) and pantograph VOFDEs. The current method incorporates Ritz and optimization techniques based on a set of wavelet functions. We use Mittag-Leffler wavelets to achieve this goal. We have developed an extra variable order (VO) Caputo pseudo-operational matrix and a pantograph operational matrix for Mittag-Leffler wavelets as new achievements. Using these matrices, along with Ritz and optimization methods, we determine an approximate solution for each of the considered problems. An estimate of errors is proposed, and numerical experiments are performed to demonstrate the performance and high accuracy of the current approach.