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<p>The current study pursues the specific goal of determining the approximate solution of the linear stochastic fractional Itô-Volterra integral equations which has been caused by fractional Brownian motion under Hurst parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2116_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mn>0</mn> <mo>&lt;</mo> <mi>H</mi> <mo>&lt;</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$0 &lt; H&lt; 1$</EquationSource> </InlineEquation>, using a numerical approach. The obtained results are based on a stochastic operational matrix of integration on generalized block-pulse basis function. In fact, we transform the equation to a linear system of algebraic equations via a lower triangular coefficients matrix from the equation, and get an approximation solution with accuracy of order <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2116_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>h</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$O(h^{2})$</EquationSource> </InlineEquation> by solving it. Then the error analysis is revealed by some theorems and definitions. Finally, an application exhibits applicability and accuracy of the method numerical.</p>

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Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numerically

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月22日

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  • Vahid Eftekhari,
  • Morteza Khodabin,
  • Mohammad Esmael Samei

摘要

The current study pursues the specific goal of determining the approximate solution of the linear stochastic fractional Itô-Volterra integral equations which has been caused by fractional Brownian motion under Hurst parameter 0 < H < 1 $0 < H< 1$ , using a numerical approach. The obtained results are based on a stochastic operational matrix of integration on generalized block-pulse basis function. In fact, we transform the equation to a linear system of algebraic equations via a lower triangular coefficients matrix from the equation, and get an approximation solution with accuracy of order O ( h 2 ) $O(h^{2})$ by solving it. Then the error analysis is revealed by some theorems and definitions. Finally, an application exhibits applicability and accuracy of the method numerical.