Résumé:
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
