This paper is primarily concerned with data analysis employing the nonlinear least squares curve fitting method and the mathematical prediction of future population growth in Bangladesh. Available actual and adjusted census data (1974–2022) of the Bangladesh population were applied in the well-known autonomous logistic population growth model and found that all data sets of the logistic (exact), Atangana-Baleanu-Caputo (ABC) fractional-order derivative approach, and logistic multi-scaling approximation fit with good agreement. Again, the existence and uniqueness of the solution for fractional-order and Hyers-Ulam stability have been studied. Generally, the growth rate and maximum environmental support of the population of any country slowly fluctuate with time. Including an approximate closed-form solution in this analysis confers several advantages in assessing population models for single species. Prior studies predominantly employed constant growth rates and carrying capacity, neglecting the investigation of fractional-order methods. Thus, the current study fills a crucial gap in the literature by introducing a more formal approach to analyzing population dynamics. Therefore, we bank on the findings of this article to contribute to accurate population forecasting and planning, national development, and national progress.

本文主要涉及采用非线性最小二乘曲线拟合方法的数据分析以及孟加拉国未来人口增长的数学预测。将孟加拉国人口的现有实际和调整后的人口普查数据（1974-2022）应用于著名的自治后勤人口增长模型，发现后勤（精确）、阿坦加纳-巴莱努-卡普托（ABC）分数的所有数据集阶导数方法和逻辑多尺度近似拟合具有良好的一致性。再次研究了分数阶稳定性和Hyers-Ulam稳定性解的存在性和唯一性。一般来说，任何国家的人口增长率和最大环境支持都会随着时间缓慢波动。在该分析中包含近似封闭式解决方案在评估单个物种的种群模型时具有多种优势。先前的研究主要采用恒定的增长率和承载能力，忽略了分数阶方法的研究。因此，当前的研究通过引入更正式的方法来分析人口动态，填补了文献中的一个关键空白。因此，我们依靠本文的研究结果为准确的人口预测和规划、国家发展和国家进步做出贡献。