Solutions of fractional order differential equations modeling temperature distribution in convective straight fins design

Advances in Difference Equations

Muhammad Sulaiman¹  Ashfaq Ahmad¹  Poom Kumam² 

[1] Department of Mathematics, Abdul Wali Khan University, 23200, Mardan, KP, Pakistan;KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan;

关键词: Fractional order differential equations;    Design engineering;    Mathematical models;    Intelligent computing techniques;    Artificial neural networks;    Heuristic optimization techniques;   

DOI  :  10.1186/s13662-021-03537-z

来源: Springer

【 摘 要 】

In this paper, the problem of temperature distribution for convective straight fins with constant and temperature-dependent thermal conductivity is solved by using artificial neural networks trained by the biogeography-based heterogeneous cuckoo search (BHCS) algorithm. We have solved the integer and noninteger order energy balance equation in order to analyse the temperature distribution in convective straight fins. We have compared our results with homotopy perturbation method (HPM), variational iteration method (VIM), and homotopy perturbation Sumudu transform method (HPSTM). The results show that the ANN–BHCS algorithm gives better results than other analytical techniques. We have further checked the efficiency of the ANN–BHCS algorithm by using the performance metrics MAD, TIC, and ENSE. We have calculated the values of MAD, TIC, and ENSE for case 1 of the problem, and histograms of these metrics show the efficiency of our algorithm.

【 授权许可】

CC BY