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<p>In this paper, we present a novel numerical algorithm for solving systems of fractional Fredholm-Volterra integro-differential equations. The proposed algorithm combines least squares support vector regression (LS-SVR), the Ritz method, and piecewise shifted Vieta-Lucas functions. Initially, we integrate operational matrices with the Ritz method and apply the Legendre-Gauss quadrature rule to formulate the problem. Subsequently, an optimization problem is constructed using the LS-SVR framework. The approximate solution is then obtained by solving this optimization problem, incorporating Lagrange multipliers. Additionally, we analyze the residual error in the Sobolev space. To demonstrate the effectiveness of the method, several numerical examples are provided, validating the proposed approach.</p>

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Ritz-least squares support vector regression technique for the system of fractional Fredholm-Volterra integro-differential equations

  • 期刊论文

  • 发表日期：

    2025年1月11日

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  • Haniye Dehestani,
  • Yadollah Ordokhani,
  • Mohsen Razzaghi

摘要

In this paper, we present a novel numerical algorithm for solving systems of fractional Fredholm-Volterra integro-differential equations. The proposed algorithm combines least squares support vector regression (LS-SVR), the Ritz method, and piecewise shifted Vieta-Lucas functions. Initially, we integrate operational matrices with the Ritz method and apply the Legendre-Gauss quadrature rule to formulate the problem. Subsequently, an optimization problem is constructed using the LS-SVR framework. The approximate solution is then obtained by solving this optimization problem, incorporating Lagrange multipliers. Additionally, we analyze the residual error in the Sobolev space. To demonstrate the effectiveness of the method, several numerical examples are provided, validating the proposed approach.