A numerical cardinal strategy to solve multi-order fractional differential equations with Caputo derivatives

Document Type : Research Paper

Authors

1 Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34148-96818, Iran

Abstract

In this article, a numerical method to solve multi-order fractional diff erential equations with Caputo derivatives is suggested. Shifted Chebyshev cardinal functions are employed as basic functions. The corresponding fractional derivative operator matrix for these cardinal functions is computed. By approximating the unknown expression of the problem in terms of the shifted Chebyshev cardinal functions, applying their fractional derivative operator matrix, and utilizing the collocation method, solving the equation under question is converted into solving a system of algebraic equations. By
solving this system, the approximate solution of the problem is obtained. Finally, the accuracy and effi ciency of the proposed method are examined by solving several numerical examples. The results show that the method presented in this article is an effi cient and highly accurate method to solve such multi-order fractional diff erential equations.

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Main Subjects

References

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https://doi.org/10.1186/s13661-024-01852-0
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History

  • Receive Date: 22 March 2025
  • Revise Date: 20 April 2026
  • Accept Date: 13 May 2026

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