修正引力中基于分数阶导数的加速宇宙数值研究

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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引用次数: 0

摘要

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。
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Numerical investigations of the fractional order derivative-based accelerating universe in the modified gravity
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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来源期刊
Modern Physics Letters A
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.
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