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Abstract
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Complex systems with memory and inherited characteristics, such as biological processes, viscoelastic materials, control systems, and anomalous diffusion, can be effectively modeled using fractional differential equations (FDEs). However, analytical solutions are uncommon and conventional numerical methods are ineffective or erroneous due to their non-local nature and reliance on the complete history of the solution. Very small time steps are frequently needed by current low-order schemes to reach acceptable accuracy, which raises the computational cost and may cause stability problems. High-order, reliable, and effective numerical techniques created especially for fractional operators are therefore highly required. These issues are resolved by creating a 4th-order Adams-Moulton predictor-corrector scheme, which allows for accurate simulation of fractional dynamics over extended periods of time by offering increased stability, improved temporal accuracy, and decreased computational effort. Establishing a dependable, high-performance framework for resolving a broad class of FDEs is what makes this research significant; it will advance theoretical research as well as real-world applications in applied mathematics, science, and engineering.
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