Theoretical analysis reveals superior error bounds for fractional Euler methods in fractional differential equations, indicating enhanced precision for numerical modeling.
The article provides a comprehensive review of advancements in the fractional Euler method, with a particular emphasis on its improved and modified versions. A detailed investigation of the method’s theoretical foundations is conducted, focusing on the analysis of error bounds. Notably, the study establishes two new error bounds and distinguishes one as superior to the other through a comparative theoretical analysis. To substantiate the theoretical findings, numerical examples are presented, offering a thorough comparison of the error bounds and reinforcing the validity of the obtained results.
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Lekshmi et al. (2026) studied this question.
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