On finding exact and approximate solutions to fractional systems of ordinary differential equations using fractional natural adomian decomposition method

Abstract

In this work, we present proofs for new theorems that deal with natural transform method (NTM) with Caputo derivative. Also, we give exact and approximate solutions to systems of fractional differential equations along with fractional ordinary and partial differential equations using the fractional natural decomposition method (FNDM). The Caputo derivative is used here to minimize the amount of computational, and this is of great significance for large-scale problems. The work outlines the significant features of the FNDM. Our work can be considered as another technique to existing methods, and will have many applications in variant areas of science and engineering.