Combining the reproducing kernel method with Taylor series expansion to solve systems of nonlinear fractional Volterra integro-differential equations
نویسندگان
1 Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran
2 Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey
3 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
4 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
doi
10.22067/ijnao.2025.90460.1542چکیده
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.
