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<p>This paper explores advanced analytical techniques for solving Burgers’ fractional partial differential equations (PDEs). We focus on the application of two innovative methods: the Aboodh transform iteration method (ATIM) and the Aboodh residual power series method (ARPSM). These methods are employed to address the complexities associated with fractional PDEs, specifically using the Caputo operator for fractional derivatives. The study provides a comprehensive analysis of the convergence and accuracy of the proposed methods through various numerical examples. We demonstrate the effectiveness of ATIM and ARPSM in yielding precise and efficient results for Burgers’ fractional partial differential equations. The results are validated against known solutions and presented in both tabular and graphical formats to illustrate the robustness of these methods. The work is an important contribution to the research of fractional calculus and nonlinear differential equations, providing useful techniques that can be used by scientists and engineers to resolve complex fractional partial differential equations with significantly better accuracy.</p>

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Innovative Aboodh-based gractional analytical methods for nonlinear Burgers’ partial differential equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月8日

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  • Naveed Iqbal,
  • Musaad S. Aldhabani,
  • Izatmand Haleemzai,
  • Hasan Nihal Zaidi,
  • Shah Hussain,
  • Safyan Mukhtar,
  • Wael W. Mohammed

摘要

This paper explores advanced analytical techniques for solving Burgers’ fractional partial differential equations (PDEs). We focus on the application of two innovative methods: the Aboodh transform iteration method (ATIM) and the Aboodh residual power series method (ARPSM). These methods are employed to address the complexities associated with fractional PDEs, specifically using the Caputo operator for fractional derivatives. The study provides a comprehensive analysis of the convergence and accuracy of the proposed methods through various numerical examples. We demonstrate the effectiveness of ATIM and ARPSM in yielding precise and efficient results for Burgers’ fractional partial differential equations. The results are validated against known solutions and presented in both tabular and graphical formats to illustrate the robustness of these methods. The work is an important contribution to the research of fractional calculus and nonlinear differential equations, providing useful techniques that can be used by scientists and engineers to resolve complex fractional partial differential equations with significantly better accuracy.