Scholarlink

<p>The study of phase lag plays an effective role in predicting what might happen during a small part of the study. It can be said that lag problems when studied in Fredholm integral equations are transformed into a mixed equation as one of the forms of the Volterra-Fredholm integral equation. The present paper is devoted to study the numerical solution of phase-lag nonlinear fractional integro-differential equations <b>(P-LNfrIo-DE)</b>. By employing the Riemann–Liouville fractional integral, the <b>P-LNfrIo-DE</b> is reduced to fractional integral equations. We therefore derive a system of nonlinear algebraic equations (<b>NAS</b>) utilizing shifted Chebyshev polynomials of the eighth type (<b>SCP8T</b>). The Banach fixed-point theorem is used to analysis the existence and uniqueness of the resulting solution to <b>P-LNfrIo-DE</b>. Additionally, the stability and convergence of the solution have been studied. Finally, some numerical examples are presented to illustrate the accuracy and efficiency of the method used. The Maple 18 program was used to establish all numerical results.</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

Stability and numerical solution for solving nonlinear fractional integro-differential equations with phase lag

  • 期刊论文

  • 发表日期：

    2025年11月28日

查看全文
  • A. M. S. Mahdy,
  • M. A. Abdou,
  • D. Sh. Mohamed

摘要

The study of phase lag plays an effective role in predicting what might happen during a small part of the study. It can be said that lag problems when studied in Fredholm integral equations are transformed into a mixed equation as one of the forms of the Volterra-Fredholm integral equation. The present paper is devoted to study the numerical solution of phase-lag nonlinear fractional integro-differential equations (P-LNfrIo-DE). By employing the Riemann–Liouville fractional integral, the P-LNfrIo-DE is reduced to fractional integral equations. We therefore derive a system of nonlinear algebraic equations (NAS) utilizing shifted Chebyshev polynomials of the eighth type (SCP8T). The Banach fixed-point theorem is used to analysis the existence and uniqueness of the resulting solution to P-LNfrIo-DE. Additionally, the stability and convergence of the solution have been studied. Finally, some numerical examples are presented to illustrate the accuracy and efficiency of the method used. The Maple 18 program was used to establish all numerical results.