Extension of the Reproducing Kernel Hilbert Space Method’s Application Range to Include Some Important Fractional Differential Equations

Abstract

Fractional differential equations are becoming more and more indispensable for modeling real-life problems. Modeling and then analyzing these fractional differential equations assists researchers in comprehending and predicting the system they want to study. This is only conceivable when their solutions are available. However, the majority of fractional differential equations lack exact solutions, and even when they do, they cannot be assessed precisely. Therefore, in order to analyze the symmetry analysis and acquire approximate solutions, one must rely on numerical approaches. In order to solve several significant fractional differential equations numerically, this work presents an effective approach. This method’s versatility and simplicity are its key benefits. To verify the RKHSM’s applicability, the convergence analysis and error estimations related to it are discussed. We also provide the profiles of a variety of representative numerical solutions to the problem at hand. We validated the potential, reliability, and efficacy of the RKHSM by testing some examples.

Keywords

• numerical solution
• non-linear fractional ordinary differential equations
• reproducing kernel method
• Caputo derivative