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Abstract
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Fractional differential equations (FDEs) are increasingly important for modeling anomalous diffusion, viscoelastic systems, control processes, and other memory-dependent phenomena in physics, engineering, and applied sciences. Their non-local fractional derivatives make analytical solutions rare, and traditional numerical methods often face challenges such as low-order accuracy, instability, or excessive computational cost, particularly for long-time simulations or stiff problems. This creates a strong necessity for high-order, stable, and efficient numerical techniques tailored for fractional dynamics. The development of a 4th-order Adams-type predictor-corrector method addresses these challenges by providing enhanced temporal accuracy, improved stability, and efficient handling of fractional derivatives. The importance of this research lies in establishing a robust, high-performance computational framework that advances both the theoretical study and practical simulation of fractional differential equations, enabling precise modeling of complex memory-dependent systems in various scientific and engineering applications.
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