Combining the reproducing kernel method with Taylor series expansion to solve systems of nonlinear fractional Volterra integro-differential equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 13، دوره 15، Issue 3 - شماره پیاپی 34، آذر 2025، صفحه 1210-1240   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.90460.1542

نویسندگان

T. Amoozad¹؛ S. Abbasbandy^{* 2}؛ H. Sahihi¹؛ T. Allahviranloo³

¹Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

²Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.

³Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey.

چکیده

In this article, we present a novel approach for solving systems of nonlinear fractional Volterra integro-differential equations $(NFVI-DEs)$ by reproducing the Hilbert kernel method. Kernel methods are powerful tools for addressing both linear and nonlinear problems. The reproducing kernel method stands out for its wide-ranging applications in solving complex scientific challenges. Our method combines the reproducing kernel method with a truncated Taylor series expansion, resulting in a more precise solution. This transformation converts the original $NFVI-DEs$ into a system of nonlinear fractional differential equations. Our numerical results showcase this approach’s effectiveness and align with theorems about error analysis.

کلیدواژه‌ها

Reproducing kernel method؛ Fractional Volterra integro-differential equations؛ Taylor series expansion؛ Error analysis

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