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<p>This paper introduces a computational approach for solving a specific type of system of non-linear fractional Volterra integro-differential equations. The proposed method is based on a newly derived formula for the Caputo fractional derivative. By utilizing this technique, the system can be transformed into a set of algebraic equations that can be easily solved using common numerical approaches. Also, the existence and uniqueness of the solution are addressed in this study. Additionally, an investigation into the error analysis of this algorithm is conducted. Furthermore, several examples are provided to demonstrate the effectiveness of the proposed scheme and compared with some other well-known methods such as iterative multi-step kernel method, Bernoulli wavelet approximation method, and Chebyshev pseudo-spectral method. The conclusions reached from this approach are highly promising and the obtained results are closely resemble to the exact solution.</p>

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A novel numerical approach based on the Bell polynomials for solving system of fractional Volterra integro-differential equations

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • Najmeh Kasaei,
  • Esmail Hesameddini,
  • Mohammad Nabati

摘要

This paper introduces a computational approach for solving a specific type of system of non-linear fractional Volterra integro-differential equations. The proposed method is based on a newly derived formula for the Caputo fractional derivative. By utilizing this technique, the system can be transformed into a set of algebraic equations that can be easily solved using common numerical approaches. Also, the existence and uniqueness of the solution are addressed in this study. Additionally, an investigation into the error analysis of this algorithm is conducted. Furthermore, several examples are provided to demonstrate the effectiveness of the proposed scheme and compared with some other well-known methods such as iterative multi-step kernel method, Bernoulli wavelet approximation method, and Chebyshev pseudo-spectral method. The conclusions reached from this approach are highly promising and the obtained results are closely resemble to the exact solution.