Advancing differential equation solutions: A novel Laplace-reproducing kernel Hilbert space method for nonlinear fractional Riccati equations

Abstract

Fractional ordinary differential equations are crucial for modeling various phenomena in engineering and physics. This study aims to enhance solution methodologies by combining the Laplace transform with the reproducing kernel Hilbert space method (RKHSM). This integration leads to a more effective approach compared to the classical RKHSM. We apply the Laplace-reproducing kernel Hilbert space method (L-RKHSM) to develop novel numerical solutions for nonlinear fractional Riccati differential equations. The L-RKHSM systematically produces both approximate and analytic solutions in series form. We present detailed results for four illustrative examples, showcasing the superior performance of the L-RKHSM over traditional methods. This innovative approach not only advances our understanding of nonlinear fractional ordinary differential equations but also demonstrates its effectiveness through significantly improved outcomes in various applications.