A new fractional modified exponential curve model and its applications

References

• Abdullah, W. S. 2009. Exponential model for predicting the sorption isotherms-evaluation, statistical approach and comparison with existing models. Jordan Journal of Civil Engineering 3 (4):344–55.
   Google Scholar
• Bi, J., H. T. Yuan, S. Duanmu, M. C. Zhou, and A. Abusorrah. 2021. Energy-optimized partial computation offloading in mobile-edge computing with genetic simulated-annealing-based particle swarm optimization. IEEE Internet of Things Journal 8 (5):3774–85. doi:10.1109/JIOT.2020.3024223.
   Web of Science ®Google Scholar
• Bi, J., H. T. Yuan, and M. C. Zhou. 2019. Temporal prediction of multiapplication consolidated workloads in distributed clouds. IEEE Transactions on Automation Science and Engineering 16 (4):1763–73. doi:10.1109/TASE.2019.2895801.
   Web of Science ®Google Scholar
• Cao, Y. L., H. Zhang, W. F. Li, M. C. Zhou, Y. Zhang, and W. A. Chaovalitwongse. 2019. Comprehensive learning particle swarm optimization algorithm with local search for multimodal functions. IEEE Transactions on Evolutionary Computation 23 (4):718–31. doi:10.1109/TEVC.2018.2885075.
   Web of Science ®Google Scholar
• Chen, L., Z. B. Liu, and N. N. Ma. 2018. Time delayed polynomial grey system model with the fractional order accumulation. Mathematical Problems in Engineering 2018:3640625. doi:10.1155/2018/3640625.
   Web of Science ®Google Scholar
• Deng, J. L. 1982. Control problems of grey systems. Systems & Control Letters 1 (5):288–94.
   Web of Science ®Google Scholar
• Duan, H. M., G. R. Lei, and K. L. Shao. 2018. Forecasting crude oil consumption in China using a grey prediction model with an optimal fractional-order accumulating operator. Complexity 2018:3869619. doi:10.1155/2018/3869619.
   Google Scholar
• Duan, H. M., K. L. Shao, X. P. Xiao, and J. W. Yang. 2017. Research on the stability of NDGM model with the fractional order accumulation and its optimization. Mathematical Problems in Engineering 2017:9728587. doi:10.1155/2017/9728587.
   Web of Science ®Google Scholar
• Gao, S., M. Zhou, Y. Wang, J. Cheng, H. Yachi, and J. Wang. 2019. Dendritic neuron model with effective learning algorithms for classification, approximation, and prediction. IEEE Transactions on Neural Networks and Learning Systems 30 (2):601–14.
   PubMed Web of Science ®Google Scholar
• Hou, X., K. Wang, C. Zhong, and Z. Wei. 2021. ST-Trader: A spatial-temporal deep neural network for modeling stock market movement. IEEE/CAA Journal of Automatica Sinica 8 (5):1015–24. doi:10.1109/JAS.2021.1003976.
   Google Scholar
• Jia, J. P., X. Q. He, and J. Y. Jin. 2019. Statistics, 7th ed. Beijing: China Renmin University Press.
   Google Scholar
• Kennedy, J., and R. Eberhart. 1995. Particle swarm optimization. In International Conference on Neural Networks, 1942–48.
   Google Scholar
• Kumar, U., and V. K. Jain. 2010. Time series models (Grey-Markov, Grey Model with rolling mechanism and singular spectrum analysis) to forecast energy consumption in India. Energy 35 (4):1709–16. doi:10.1016/j.energy.2009.12.021.
   Web of Science ®Google Scholar
• Lao, W. J., K. A. Maruya, and D. Tsukada. 2019. An exponential model based new approach for correcting aqueous concentrations of hydrophobic organic chemicals measured by polyethylene passive samplers. Science of the Total Environment 646:11–18. doi:10.1016/j.scitotenv.2018.07.192.
   PubMed Web of Science ®Google Scholar
• Mao, M. Z., and E. C. Chirwa. 2006. Application of grey model GM(1,1) to vehicle fatality risk estimation. Technological Forecasting and Social Change 73 (5):588–605. doi:10.1016/j.techfore.2004.08.004.
   Web of Science ®Google Scholar
• Meng, W., D. L. Yang, and H. Huang. 2018. Prediction of China’s sulfur dioxide emissions by discrete grey model with fractional order generation operators. Complexity 2018:8610679. doi:10.1155/2018/8610679.
   Google Scholar
• Morita, H., T. Kase, Y. Tamura, and S. Iwamoto. 1996. Interval prediction of annual maximum demand using grey dynamic model. International Journal of Electrical Power & Energy Systems 18 (7):409–13. doi:10.1016/0142-0615(95)00019-4.
   Web of Science ®Google Scholar
• Pan, J., C. B. Li, Y. Tang, W. Li, and X. O. Li. 2021. Energy consumption prediction of a CNC machining process with incomplete data. IEEE/CAA Journal of Automatica Sinica 8 (5):987–1000. doi:10.1109/JAS.2021.1003970.
   Google Scholar
• Tan, S. Y. 2019. An exponential curve with oscillating term and its application in China’s primary energy consumption. Operations Research and Fuzziology 9 (2):235–42.
   Google Scholar
• Tang, J., G. Liu, and Q. T. Pan. 2021. A review on representative swarm intelligence algorithms for solving optimization problems: Applications and trends. IEEE/CAA Journal of Automatica Sinica 8 (10):1627–43. doi:10.1109/JAS.2021.1004129.
   Google Scholar
• Trelea, I. C. 2003. The particle swarm optimization algorithm: Convergence analysis and parameter selection. Information Processing Letters 85 (6):317–25. doi:10.1016/S0020-0190(02)00447-7.
   Web of Science ®Google Scholar
• Wang, W., J. M. Zai, and T. H. Lu. 2008. Analysis on hyperbolic model and exponential model for post-construction settlement of soft soil. Journal of Jiangsu University (Natural Science Edition) 29 (2):173–76.
   Google Scholar
• Wu, L. F., S. F. Liu, L. G. Yao, S. L. Yan, and D. L. Liu. 2013. Grey system model with the fractional order accumulation. Communications in Nonlinear Science and Numerical Simulation 18 (7):1775–85. doi:10.1016/j.cnsns.2012.11.017.
   Web of Science ®Google Scholar
• Ying, Z. M., J. Zhang, and Y. Q. Shang. 2005. Exponential model for simulating load-displacement curve of anchor rod. Rock and Soil Mechanics 26 (8):1331–34.
   Google Scholar
• Zhang, P., and F. Luo. 2019. An improved exponential curve model and its application in the total water resources in Tibet Autonomous region. Operations Research and Fuzziology 9 (4):235–42.
   Google Scholar
• Zhou, J. Z., R. C. Fang, Y. H. Li, Y. C. Zhang, and B. Peng. 2009. Parameter optimization of nonlinear grey Bernoulli model using particle swarm optimization. Applied Mathematics and Computation 207 (2):292–99. doi:10.1016/j.amc.2008.10.045.
   Web of Science ®Google Scholar
• Zhou, Y. D., H. Q. Wang, and W. Y. Lv. 2016. Time series analysis and its application. Beijing: High Education Press.
   Google Scholar
• Zuo, K., Y. L. Zhang, H. Li, and W. Q. Wu. 2019. Research on an exponential curve with first order term of time. Operations Research and Fuzziology 9 (3):235–42.
   Google Scholar