Combined Adomian Decomposition Method with Integral Transform

At present, three numerical solution methods have mainly been used to solve fractional-order chaotic systems in the literature: frequency domain approximation, predictor–corrector approach and Adomian decomposition method (ADM). Based on literature, ADM is capable of dealing with linear nonlinear problems a time domain. Also, (ADM) among efficient approaches for solving non-linear equations. Numerical one critical theoretical research applications systems. The decomposed into an infinite series integral transformation differential equation implemented this work. Furthermore, can be thought as that converges exact solution. aim study combine different transformation, including Laplace, Sumudu, Natural, Elzaki, Mohand, Kashuri-Fundo. study's key finding employing combined fractional ordinary equations yields good results. main contribution our shows considered produce excellent performance Therefore, proposed has practical implications order science social sciences, such analytical solutions secure communication system, biological financial risk models, physics phenomenon, neuron models engineering application.