Scholarlink

<p>In this paper, the Tantawy Least Square Method (TLSM) is presented and used to achieve approximate solutions to fractional-order partial differential equations (FPDEs) with the Caputo derivative. The suggested method is a combination of the least squares approximation and Tantawy decomposition framework, which ensures minimal residual error and maximum accuracy. To show its efficiency, TLSM is implemented on a set of test problems, among them the fractional Kolmogorov equation, the linearized Korteweg-de Vries (KdV) equation, and the nonlinear KdV equation. The results obtained are compared to the known techniques including the fractional reduced differential transform method (FRDTM) and the differential transform method (DTM). Experimental results indicate that TLSM produces solutions with minimal absolute errors and hence is more precise and stable than available methods. Moreover, the fractional order is also found to be important as the analysis demonstrates that the order parameter has an influential effect on the diffusion rates, memory effects, and nonlinear wave structures. These results make TLSM a dependable and effective tool to tackle linear and nonlinear FPDEs, and may be extended to multidimensional and coupled systems to applied sciences and engineering.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Novel analysis of linear and nonlinear fractional KdV and Kolmogorov equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月8日

查看全文
  • Abdullah A. Zaagan,
  • Musawa Yahya Almusawa,
  • Hamad Zogan,
  • Hamdan Alshehri,
  • Fathe Jeribi

摘要

In this paper, the Tantawy Least Square Method (TLSM) is presented and used to achieve approximate solutions to fractional-order partial differential equations (FPDEs) with the Caputo derivative. The suggested method is a combination of the least squares approximation and Tantawy decomposition framework, which ensures minimal residual error and maximum accuracy. To show its efficiency, TLSM is implemented on a set of test problems, among them the fractional Kolmogorov equation, the linearized Korteweg-de Vries (KdV) equation, and the nonlinear KdV equation. The results obtained are compared to the known techniques including the fractional reduced differential transform method (FRDTM) and the differential transform method (DTM). Experimental results indicate that TLSM produces solutions with minimal absolute errors and hence is more precise and stable than available methods. Moreover, the fractional order is also found to be important as the analysis demonstrates that the order parameter has an influential effect on the diffusion rates, memory effects, and nonlinear wave structures. These results make TLSM a dependable and effective tool to tackle linear and nonlinear FPDEs, and may be extended to multidimensional and coupled systems to applied sciences and engineering.