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<p>This study presents a machine learning approach using least squares support vector regression (LS-SVR) for solving fractional pantograph differential equations involving the left-sided Bessel fractional (LSBF) derivative. First, a new orthonormal basis, called the fractional-order airfoil functions (FAFs) is constructed. Then, the unknown function and its derivatives are approximated via FAFs. The collocation LS-SVR method is applied to train the network with the FAF kernel. The method’s formulation results in an optimization problem that an equivalent system of algebraic equations is derived. Finally, the error analysis of method is presented and numerical tests are provided to show the efficiency of the suggested technique.</p>

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Fractional-order least squares support vector regression to solve left-sided Bessel fractional pantograph differential equations

  • 期刊论文

  • 发表日期：

    2025年3月23日

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  • Parisa Rahimkhani,
  • Nasrin Samadyar,
  • Hossein Hassani

摘要

This study presents a machine learning approach using least squares support vector regression (LS-SVR) for solving fractional pantograph differential equations involving the left-sided Bessel fractional (LSBF) derivative. First, a new orthonormal basis, called the fractional-order airfoil functions (FAFs) is constructed. Then, the unknown function and its derivatives are approximated via FAFs. The collocation LS-SVR method is applied to train the network with the FAF kernel. The method’s formulation results in an optimization problem that an equivalent system of algebraic equations is derived. Finally, the error analysis of method is presented and numerical tests are provided to show the efficiency of the suggested technique.