Scholarlink

<p>We perform a Lie point symmetry analysis of a time-fractional potential Korteweg–de Vries (FP-KdV) equation with the Riemann–Liouville derivative. By transforming the dependent variable, we map the time-fractional FP-KdV equation to a nonlinear ordinary differential equation (ODE) of fractional order using underlying symmetry generators. We obtain the derivative in the Erdélyi–Kober operator. We then construct the solution of the reduced fractional ODE by applying the power series method. The conservation laws (CLs) for the time-fractional FP-KdV equation are determined via Ibragimov’s non-local conservation method to time-fractional partial differential equations (FPDEs). Solutions for FPDEs via CLs have yet to be explored. Additionally, we present graphical representations of the results obtained using the power series solution method.</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

On the invariant analysis and integrability of the time-fractional potential KdV equation

  • 期刊论文

  • 发表日期：

    2025年7月16日

查看全文
  • Aneeqa Ihsan,
  • Akhtar Hussain,
  • A. H. Kara,
  • F. D. Zaman

摘要

We perform a Lie point symmetry analysis of a time-fractional potential Korteweg–de Vries (FP-KdV) equation with the Riemann–Liouville derivative. By transforming the dependent variable, we map the time-fractional FP-KdV equation to a nonlinear ordinary differential equation (ODE) of fractional order using underlying symmetry generators. We obtain the derivative in the Erdélyi–Kober operator. We then construct the solution of the reduced fractional ODE by applying the power series method. The conservation laws (CLs) for the time-fractional FP-KdV equation are determined via Ibragimov’s non-local conservation method to time-fractional partial differential equations (FPDEs). Solutions for FPDEs via CLs have yet to be explored. Additionally, we present graphical representations of the results obtained using the power series solution method.