Numerical solutions for systems of nonlinear fractional differential equations using the fractional natural decomposition method
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Abstract
This paper presents a complete study of the Fractional Natural Decomposition Method (FNDM) for solving systems of nonlinear fractional ordinary differential equations. The FNDM combines the Natural Transform Method with the Adomian Decomposition Method to construct analytical approximate solutions. We provide a detailed exposition of the methodology, theoretical foundations including existence, uniqueness, and convergence theorems, and applications to five distinct nonlinear systems. Recursive relations, Adomian polynomials, and numerical results are presented. Graphs illustrate the behavior of approximate solutions for different fractional orders. The results demonstrate the efficiency, accuracy, and versatility of the FNDM.
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