Numerical investigations of the fractional order derivative-based accelerating universe in the modified gravity

IF 1.5 4区物理与天体物理 Q3 ASTRONOMY & ASTROPHYSICS

Modern Physics Letters A Pub Date : 2024-01-06 DOI:10.1142/s0217732323501808

A. Alderremy, J. Gómez-Aguilar, Z. Sabir, Muhammad Asif Zahoor Raja, Shaban Aly

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Abstract

In this work, a Liouville–Caputo fractional order (FO) derivative for the mathematical system based on the accelerating universe in the modified gravity (AUMG), i.e. FO-AUMG is proposed to get more accurate solutions. The nonlinear dynamics of the FO-AUMG is classified into five dynamics. The performances of the designed nonlinear FO-AUMG are numerically stimulated with the stochastic procedures of Levenberg–Marquardt backpropagated (LMB) scheme-based neural networks. The statics for FO-AUMS is used for the nonlinear FO-AUMG as 72%, 16% and 12% for training, authorization, and testing. Twenty neurons in hidden layers have been used to approximate the solution of the nonlinear FO-AUMS. The comparison of three different cases of the nonlinear FO-AUMS is performed with dataset generated by Adams method. To validate the uniformity, legitimacy, precision, and competence of LMB-based adaptive neural networks, the outcomes of the state transitions parameters, regression, correlation, error-histogram plots have been exploited.

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修正引力中基于分数阶导数的加速宇宙数值研究

本研究提出了基于修正重力加速宇宙（AUMG）数学系统的 Liouville-Caputo 分数阶（FO）导数，即 FO-AUMG，以获得更精确的解。FO-AUMG 的非线性动力学分为五个动力学。利用基于 Levenberg-Marquardt 反向传播（LMB）方案的神经网络随机程序对所设计的非线性 FO-AUMG 的性能进行了数值激励。在非线性 FO-AUMG 的训练、授权和测试中，FO-AUMS 的统计量分别为 72%、16% 和 12%。隐藏层中的 20 个神经元被用来近似非线性 FO-AUMS 的解决方案。利用亚当斯方法生成的数据集对非线性 FO-AUMS 的三种不同情况进行了比较。为了验证基于 LMB 的自适应神经网络的统一性、合理性、精确性和能力，我们利用了状态转换参数、回归、相关性、误差-柱状图等结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Modern Physics Letters A 物理-物理：核物理

CiteScore

3.10

自引率

7.10%

发文量

186

审稿时长

3 months

期刊介绍： This letters journal, launched in 1986, consists of research papers covering current research developments in Gravitation, Cosmology, Astrophysics, Nuclear Physics, Particles and Fields, Accelerator physics, and Quantum Information. A Brief Review section has also been initiated with the purpose of publishing short reports on the latest experimental findings and urgent new theoretical developments.