Reproducing Kernel Hilbert Space Method For Solving Fractional Integro-Differential Systems

Abstract

This dissertation develops an efficient numerical method for solving fractional integro differential systems involving the Caputo fractional derivative. The proposed approach employs the Reproducing Kernel Hilbert Space (RKHS) method to construct ap proximate solutions expressed as uniformly convergent series, ensuring both high accuracy and rapid convergence. Numerical examples demonstrate the effectiveness and precision of the RKHS method in addressing complex fractional systems. The results reveal the significant impact of the fractional derivative order on the qualitative behavior of the solu tions, underscoring the importance of fractional calculus in modeling memory-dependent phenomena. This study establishes the RKHS method as a robust and promising tool for the numerical analysis of fractional systems. Future work may extend this framework to incorporate other types of fractional derivatives, higher-dimensional problems, and systems with more intricate initial and boundary conditions