531
Views
36
CrossRef citations to date
0
Altmetric
Original Articles

A new artificial neural network structure for solving high-order linear fractional differential equations

&
Pages 528-539 | Received 23 Feb 2016, Accepted 02 Feb 2017, Published online: 28 Feb 2017

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (3)

Saeed Althubiti, Manoj Kumar, Pranay Goswami & Kranti Kumar. (2023) Artificial neural network for solving the nonlinear singular fractional differential equations. Applied Mathematics in Science and Engineering 31:1.
Read now
Zhanying Yang & Jie Zhang. (2020) Global stabilization of fractional-order bidirectional associative memory neural networks with mixed time delays via adaptive feedback control. International Journal of Computer Mathematics 97:10, pages 2074-2090.
Read now
Syed Tauseef Mohyud-Din, Sadaf Bibi, Naveed Ahmed & Umar Khan. (2019) Some exact solutions of the nonlinear space–time fractional differential equations. Waves in Random and Complex Media 29:4, pages 645-664.
Read now

Articles from other publishers (33)

Faouzi Haddouchi & Mohammad Esmael Samei. (2024) Solvability of a generalized -Riemann–Liouville fractional BVP under nonlocal boundary conditions . Mathematics and Computers in Simulation 219, pages 355-377.
Crossref
Sivalingam S M, Pushpendra Kumar & V. Govindaraj. (2023) A novel optimization-based physics-informed neural network scheme for solving fractional differential equations. Engineering with Computers 40:2, pages 855-865.
Crossref
Ziqing Yang, Ruiping Niu, Miaomiao Chen, Hongen Jia & Shengli Li. (2024) Adaptive fractional physical information neural network based on PQI scheme for solving time-fractional partial differential equations. Electronic Research Archive 32:4, pages 2699-2727.
Crossref
Hongling Qiu, Iakov Korovin, Heng Liu, Sergey Gorbachev, Nadezhda Gorbacheva & Jinde Cao. (2024) Distributed adaptive neural network consensus control of fractional-order multi-agent systems with unknown control directions. Information Sciences 655, pages 119871.
Crossref
Sivalingam S M, Pushpendra Kumar & Venkatesan Govindaraj. (2023) A neural networks-based numerical method for the generalized Caputo-type fractional differential equations. Mathematics and Computers in Simulation 213, pages 302-323.
Crossref
A. M. Shloof, A. Ahmadian, N. Senu, Soheil Salahshour, S. N. I. Ibrahim & M. Pakdaman. (2023) A highly accurate artificial neural networks scheme for solving higher multi‐order fractal‐fractional differential equations based on generalized Caputo derivative. International Journal for Numerical Methods in Engineering 124:19, pages 4371-4404.
Crossref
Jinde Cao, K. Udhayakumar, R. Rakkiyappan, Xiaodi Li & Jianquan Lu. (2023) A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks. IEEE Transactions on Neural Networks and Learning Systems 34:9, pages 5476-5496.
Crossref
Ioannis G. Tsoulos & Alexandros Tzallas. (2023) Training Artificial Neural Networks Using a Global Optimization Method That Utilizes Neural Networks. AI 4:3, pages 491-508.
Crossref
T. Allahviranloo, A. Jafarian, R. Saneifard, N. Ghalami, S. Measoomy Nia, F. Kiani, U. Fernandez-Gamiz & S. Noeiaghdam. (2023) An application of artificial neural networks for solving fractional higher-order linear integro-differential equations. Boundary Value Problems 2023:1.
Crossref
Yanfei Lu, Shiqing Zhang, Futian Weng & Hongli Sun. (2023) Approximate solutions to several classes of Volterra and Fredholm integral equations using the neural network algorithm based on the sine-cosine basis function and extreme learning machine. Frontiers in Computational Neuroscience 17.
Crossref
Mohd Rashid Admon, Norazak Senu, Ali Ahmadian, Zanariah Abdul Majid & Soheil Salahshour. (2023) A new efficient algorithm based on feedforward neural network for solving differential equations of fractional order. Communications in Nonlinear Science and Numerical Simulation 117, pages 106968.
Crossref
A. M. Shloof, N. Senu, A. Ahmadian, M. Pakdaman & S. Salahshour. (2022) A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense. Engineering with Computers 39:1, pages 505-515.
Crossref
Mingqiu Wu, Jinlei Zhang, Zhijie Huang, Xiang Li & Yumin Dong. (2021) Numerical solutions of wavelet neural networks for fractional differential equations. Mathematical Methods in the Applied Sciences 46:3, pages 3031-3044.
Crossref
Yinlin Ye, Hongtao Fan, Yajing Li, Ao Huang & Weiheng He. (2023) An artificial neural network approach for a class of time-fractional diffusion and diffusion-wave equations. Networks and Heterogeneous Media 18:3, pages 1083-1104.
Crossref
He Zhang, Ravi Srinivasan, Xu Yang, Sherry Ahrentzen, Eric S. Coker & Aladdin Alwisy. (2022) Factors influencing indoor air pollution in buildings using PCA-LMBP neural network: A case study of a university campus. Building and Environment 225, pages 109643.
Crossref
Shupeng Wang, Hui Zhang & Xiaoyun Jiang. (2022) Fractional physics-informed neural networks for time-fractional phase field models. Nonlinear Dynamics 110:3, pages 2715-2739.
Crossref
R. Saneifard, A. Jafarian, N. Ghalami & S. Measoomy Nia. (2022) Extended artificial neural networks approach for solving two-dimensional fractional-order Volterra-type integro-differential equations. Information Sciences 612, pages 887-897.
Crossref
Yanfei Lu, Futian Weng & Hongli Sun. (2022) Numerical solution for high-order ordinary differential equations using H-ELM algorithm. Engineering Computations 39:7, pages 2781-2801.
Crossref
Ahmad Jafarian, Rezvan Rezaei & Alireza Khalili Golmankhaneh. (2022) On Solving Fractional Higher-Order Equations via Artificial Neural Networks. Iranian Journal of Science and Technology, Transactions A: Science 46:2, pages 535-545.
Crossref
Babak Shiri, Hua Kong, Guo-Cheng Wu & Cheng Luo. (2022) Adaptive Learning Neural Network Method for Solving Time–Fractional Diffusion Equations. Neural Computation 34:4, pages 971-990.
Crossref
Pingfei Dai & Xiangyu Yu. (2022) An Artificial Neural Network Approach for Solving Space Fractional Differential Equations. Symmetry 14:3, pages 535.
Crossref
Hongliang Liu, Huini Liu, Jie Xu, Lijuan Li & Jingwen Song. (2021) Jacobi Neural Network Method for Solving Linear Differential-Algebraic Equations with Variable Coefficients. Neural Processing Letters 53:5, pages 3357-3374.
Crossref
Mdi B. Jeelani, Abdulkafi M. Saeed, Mohammed S. Abdo & Kamal Shah. (2021) Positive solutions for fractional boundary value problems under a generalized fractional operator. Mathematical Methods in the Applied Sciences 44:11, pages 9524-9540.
Crossref
Haidong Qu, Zihang She & Xuan Liu. (2021) Neural network method for solving fractional diffusion equations. Applied Mathematics and Computation 391, pages 125635.
Crossref
Hao Zhang, Yong Xu, Yongge Li & Jürgen Kurths. (2020) Statistical solution to SDEs with $$\alpha $$-stable Lévy noise via deep neural network. International Journal of Dynamics and Control 8:4, pages 1129-1140.
Crossref
Haidong Qu, Xuan Liu & Zihang She. (2020) Neural network method for fractional-order partial differential equations. Neurocomputing.
Crossref
Yanfei Lu, Gang Chen, Qingfei Yin, Hongli Sun & Muzhou Hou. (2020) Solving the ruin probabilities of some risk models with Legendre neural network algorithm. Digital Signal Processing 99, pages 102634.
Crossref
Amir Hosein Hadian Rasanan, Nastaran Bajalan, Kourosh Parand & Jamal Amani Rad. (2019) Simulation of nonlinear fractional dynamics arising in the modeling of cognitive decision making using a new fractional neural network. Mathematical Methods in the Applied Sciences 43:3, pages 1437-1466.
Crossref
Sergio Ledesma, Dora-Luz Almanza-Ojeda, Mario-Alberto Ibarra-Manzano, Eduardo Cabal Yepez, Juan Gabriel Avina-Cervantes & Pascal Fallavollita. (2020) Differential Neural Networks (DNN). IEEE Access 8, pages 156530-156538.
Crossref
Shakir Al-Busultan, Gafel Kareem Aswed, Raid R. A. Almuhanna & Sajjad E. Rasheed. (2020) Application of Artificial Neural Networks in Predicting Subbase CBR Values Using Soil Indices Data. IOP Conference Series: Materials Science and Engineering 671:1, pages 012106.
Crossref
Yanfei Lu, Qingfei Yin, Hongyi Li, Hongli Sun, Yunlei Yang & Muzhou Hou. (2019) The LS-SVM algorithms for boundary value problems of high-order ordinary differential equations. Advances in Difference Equations 2019:1.
Crossref
Dmitry A. Tarkhov, Maksim A. Migovan, Kirill A. Ivanenko, Sergey A. Smirnov & Aleksandra M. Kobicheva. 2019. Digital Science. Digital Science 450 455 .
Yunlei Yang, Muzhou Hou & Jianshu Luo. (2018) A novel improved extreme learning machine algorithm in solving ordinary differential equations by Legendre neural network methods. Advances in Difference Equations 2018:1.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.