Solutions of Nonlinear Fractional-Order Differential Equation Systems Using a Numerical Technique - Mohammed Boukedroun; Souad Ayadi; Fouzia Chita; Meltem Erden Ege; Ozgur Ege; Rajagopalan Ramaswamy (Axioms)
The primary objective of this study is to expand the application of analytical and numerical methods for solving nonlinear Systems of Fractional Differential Equations (SFDEs) with Caputo fractional derivatives (CFDs) under initial conditions. Our proposed approach, the Multistage Telescoping Decomposition Elzaki Method (MTDEM), integrates the advantages of the Elzaki transform with the Multistage Telescoping Decomposition Method (MTDM), significantly enhancing the efficiency of the solution process and improving the convergence rate. Additionally, it simplifies computational operations and reduces the computational complexity associated with solving these nonlinear systems. A comprehensive comparison is conducted to highlight the accuracy and computational advantages of our proposed method compared to existing techniques, including the exact solution and the Telescoping Decomposition Method (TDM), through numerical examples that demonstrate the effectiveness of the proposed approach. The flexibility of the MTDEM allows for its application in a wide range of nonlinear SFDEs, making it a valuable tool in various scientific and engineering fields. These systems are widely used in modeling numerous physical, biological, and economic phenomena, such as the dynamics of electrical systems, heat transfer, and population growth models, underscoring the importance of developing accurate and efficient computational methods for their solutions. Through this study, we present a novel contribution to enhancing numerical and analytical techniques, paving the way for broader applications in multiple domains that require precise and reliable solutions for complex fractional systems.