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<p>The main purpose of this article is to propose a Krawtchouk Wavelets Method (KWM) in conjunction with a collocation method to solve two delayed models of linear and nonlinear differential equations (constant and proportional delay) of fractional-order. For the proposed scheme, first we introduce the novel Krawtchouk Wavelets (KWs) on an arbitrary interval, and then closed-form of fractional integral of KWs is constructed. The mention models are transformed into algebraic equations by utilizing the collocation method and vector of fractional integral of KWs. To prove the error analysis and convergence of the recommended method, several theorems are presented. Finally, some examples of two models are solved by the KWM to confirm the utility and validity of the suggested technique.</p>

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A Novel Design of Krawtchouk Wavelet Based Projection Approach to Solve the Nonlinear Fractional Delay Differential Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月7日

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  • Hajar Mohammadi,
  • Habibollah Saeedi,
  • Mohammad Izadi

摘要

The main purpose of this article is to propose a Krawtchouk Wavelets Method (KWM) in conjunction with a collocation method to solve two delayed models of linear and nonlinear differential equations (constant and proportional delay) of fractional-order. For the proposed scheme, first we introduce the novel Krawtchouk Wavelets (KWs) on an arbitrary interval, and then closed-form of fractional integral of KWs is constructed. The mention models are transformed into algebraic equations by utilizing the collocation method and vector of fractional integral of KWs. To prove the error analysis and convergence of the recommended method, several theorems are presented. Finally, some examples of two models are solved by the KWM to confirm the utility and validity of the suggested technique.