Résumé:
In this work, an accurate numerical approximation algorithm based on the reproducing
kernel Hilbert space (RKHS) approach has been proposed to solve a class of fractional
differential equations within the framework of the Caputo sense. The analytical solution is
presented as a convergent series with accurately computable structures in the reproducing
kernel space. The n-term approximation has been obtained and proven to converge
uniformly to the analytical solution. The main advantage of the RKHS approach is its
direct application without requiring linearization or perturbation, thereby avoiding errors
associated with discretization. Several numerical examples are provided to demonstrate
the accuracy of the computations and the effectiveness of the proposed approach. The
numerical results indicate that the RKHS method is a powerful tool for finding effective
approximated solutions to such systems arising in applied mathematics, physics, and
engineering.
