Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numerically
Abstract 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. Th...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-08-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02116-5 |
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| author | Vahid Eftekhari Morteza Khodabin Mohammad Esmael Samei |
| author_facet | Vahid Eftekhari Morteza Khodabin Mohammad Esmael Samei |
| author_sort | Vahid Eftekhari |
| collection | DOAJ |
| description | Abstract 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. |
| format | Article |
| id | doaj-art-14d985cdcf9b4262b32cf69a264f3469 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-14d985cdcf9b4262b32cf69a264f34692025-08-24T11:41:25ZengSpringerOpenBoundary Value Problems1687-27702025-08-012025112810.1186/s13661-025-02116-5Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numericallyVahid Eftekhari0Morteza Khodabin1Mohammad Esmael Samei2Department of Mathematics, Karaj Branch, Islamic Azad UniversityDepartment of Mathematics, Karaj Branch, Islamic Azad UniversityDepartment of Mathematics, Faculty of Science, Bu-Ali Sina UniversityAbstract 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.https://doi.org/10.1186/s13661-025-02116-5Fractional stochastic integral equationFractional Brownian motionOperational matrixBlock-pulse basis function |
| spellingShingle | Vahid Eftekhari Morteza Khodabin Mohammad Esmael Samei Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numerically Boundary Value Problems Fractional stochastic integral equation Fractional Brownian motion Operational matrix Block-pulse basis function |
| title | Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numerically |
| title_full | Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numerically |
| title_fullStr | Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numerically |
| title_full_unstemmed | Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numerically |
| title_short | Using block-pulse basis functions for solving the stochastic fractional integral equations with respect to fractional Brownian motion numerically |
| title_sort | using block pulse basis functions for solving the stochastic fractional integral equations with respect to fractional brownian motion numerically |
| topic | Fractional stochastic integral equation Fractional Brownian motion Operational matrix Block-pulse basis function |
| url | https://doi.org/10.1186/s13661-025-02116-5 |
| work_keys_str_mv | AT vahideftekhari usingblockpulsebasisfunctionsforsolvingthestochasticfractionalintegralequationswithrespecttofractionalbrownianmotionnumerically AT mortezakhodabin usingblockpulsebasisfunctionsforsolvingthestochasticfractionalintegralequationswithrespecttofractionalbrownianmotionnumerically AT mohammadesmaelsamei usingblockpulsebasisfunctionsforsolvingthestochasticfractionalintegralequationswithrespecttofractionalbrownianmotionnumerically |