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<p>In this paper, we introduce a category of fractional integro-differential equations involving the Caputo tempered derivative. The piecewise Chebyshev cardinal functions, as an efficient class of basis functions, are utilized to develop a computational method for these equations. To establish this method, an operational matrix is derived for the tempered fractional integral of these piecewise functions. In the proposed approach, by approximating the fractional term of the problem using the aforementioned basis functions, and applying the expressed operational matrix, a numerical solution is obtained for the problem by solving a system of algebraic equations. The convergence analysis of the developed method is investigated both theoretically and numerically. The validity of the approach is verified by solving some numerical examples.</p>

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A cardinal-based approximation approach for a family of nonlinear fractional integro-differential equations involving Caputo tempered derivative

  • 期刊论文

  • 发表日期：

    2025年2月10日

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  • M. H. Heydari,
  • Dumitru Baleanu,
  • M. Bayram

摘要

In this paper, we introduce a category of fractional integro-differential equations involving the Caputo tempered derivative. The piecewise Chebyshev cardinal functions, as an efficient class of basis functions, are utilized to develop a computational method for these equations. To establish this method, an operational matrix is derived for the tempered fractional integral of these piecewise functions. In the proposed approach, by approximating the fractional term of the problem using the aforementioned basis functions, and applying the expressed operational matrix, a numerical solution is obtained for the problem by solving a system of algebraic equations. The convergence analysis of the developed method is investigated both theoretically and numerically. The validity of the approach is verified by solving some numerical examples.