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<p>This article aims to discuss a numerical method for approximating the solution of a nonlinear system of fractional partial integro-differential equations of Volterra type. To achieve this, we develop an operational matrix based on the Hat function for fractional integration. By expanding the partial and fractional derivatives of the unknown functions in terms of two-dimensional Hat functions (2DHFs) and using the derived operational matrix, we transform the original problem into a nonlinear system. The approximate solution to the original problem can be obtained by solving this system. Additionally, we present some theorems regarding error analysis and convergence. Finally, we provide some examples to demonstrate the effectiveness and validity of the method.</p>

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Application of Hat functions to simulate coupled systems of partial two-dimensional nonlinear fractional Volterra integral equations

  • 期刊论文

  • 发表日期：

    2025年12月13日

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  • A. A. Khajehnasiri,
  • R. Ezzati,
  • M. Safavi,
  • S. Rezabeyk

摘要

This article aims to discuss a numerical method for approximating the solution of a nonlinear system of fractional partial integro-differential equations of Volterra type. To achieve this, we develop an operational matrix based on the Hat function for fractional integration. By expanding the partial and fractional derivatives of the unknown functions in terms of two-dimensional Hat functions (2DHFs) and using the derived operational matrix, we transform the original problem into a nonlinear system. The approximate solution to the original problem can be obtained by solving this system. Additionally, we present some theorems regarding error analysis and convergence. Finally, we provide some examples to demonstrate the effectiveness and validity of the method.