Numerical Solution of Two-Dimensional Variable-Order Fractional Optimal Control Problem by Generalized Polynomial Basis
Author
Abstract
Suggested Citation
DOI: 10.1007/s10957-018-1389-z
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Yang, Xiao-Jun & Machado, J.A. Tenreiro, 2017. "A new fractional operator of variable order: Application in the description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 276-283.
- Samer S. Ezz-Eldien & Ramy M. Hafez & Ali H. Bhrawy & Dumitru Baleanu & Ahmed A. El-Kalaawy, 2017. "New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 295-320, July.
- Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Hossein Hassani & Zakieh Avazzadeh & Praveen Agarwal & Mohammad Javad Ebadi & Ali Bayati Eshkaftaki, 2024. "Generalized Bernoulli–Laguerre Polynomials: Applications in Coupled Nonlinear System of Variable-Order Fractional PDEs," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 371-393, January.
- Heydari, M.H., 2020. "Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana–Baleanu–Caputo variable-order fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
- Pho, Kim-Hung & Heydari, M.H. & Tuan, Bui Anh & Mahmoudi, Mohammad Reza, 2020. "Numerical study of nonlinear 2D optimal control problems with multi-term variable-order fractional derivatives in the Atangana-Baleanu-Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
- Hosseininia, M. & Heydari, M.H., 2019. "Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 400-407.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Owolabi, Kolade M. & Atangana, Abdon, 2018. "Chaotic behaviour in system of noninteger-order ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 362-370.
- Harendra Singh & Rajesh K. Pandey & Hari Mohan Srivastava, 2019. "Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials," Mathematics, MDPI, vol. 7(3), pages 1-24, February.
- Hamid Boulares & Abdelkader Moumen & Khaireddine Fernane & Jehad Alzabut & Hicham Saber & Tariq Alraqad & Mhamed Benaissa, 2023. "On Solutions of Fractional Integrodifferential Systems Involving Ψ-Caputo Derivative and Ψ-Riemann–Liouville Fractional Integral," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
- Ghanbari, Behzad & Atangana, Abdon, 2020. "A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
- Asifa, & Kumam, Poom & Tassaddiq, Asifa & Watthayu, Wiboonsak & Shah, Zahir & Anwar, Talha, 2022. "Modeling and simulation based investigation of unsteady MHD radiative flow of rate type fluid; a comparative fractional analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 486-507.
- Hassani, Hossein & Avazzadeh, Zakieh, 2019. "Transcendental Bernstein series for solving nonlinear variable order fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
- Zhenduo Sun & Nengneng Qing & Xiangzhi Kong, 2023. "Asymptotic Hybrid Projection Lag Synchronization of Nonidentical Variable-Order Fractional Complex Dynamic Networks," Mathematics, MDPI, vol. 11(13), pages 1-17, June.
- Bohaienko, Vsevolod & Gladky, Anatolij & Romashchenko, Mykhailo & Matiash, Tetiana, 2021. "Identification of fractional water transport model with ψ-Caputo derivatives using particle swarm optimization algorithm," Applied Mathematics and Computation, Elsevier, vol. 390(C).
- Ayazi, N. & Mokhtary, P. & Moghaddam, B. Parsa, 2024. "Efficiently solving fractional delay differential equations of variable order via an adjusted spectral element approach," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
- Campos, Rafael G. & Huet, Adolfo, 2018. "Numerical inversion of the Laplace transform and its application to fractional diffusion," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 70-78.
- Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
- Hassani, Hossein & Naraghirad, Eskandar, 2019. "A new computational method based on optimization scheme for solving variable-order time fractional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 1-17.
- Paul Hauseux & Jack S Hale & Stéphane P A Bordas, 2017. "Calculating the Malliavin derivative of some stochastic mechanics problems," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-18, December.
- Razminia, Kambiz & Razminia, Abolhassan & Baleanu, Dumitru, 2019. "Fractal-fractional modelling of partially penetrating wells," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 135-142.
- Tarasov, Vasily E. & Tarasova, Valentina V., 2018. "Macroeconomic models with long dynamic memory: Fractional calculus approach," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 466-486.
- Baghani, Omid, 2022. "SCW-iterative-computational method for solving a wide class of nonlinear fractional optimal control problems with Caputo derivatives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 540-558.
- Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
- dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
- Sheng Zhang & Yuanyuan Wei & Bo Xu, 2019. "Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example," Complexity, Hindawi, vol. 2019, pages 1-9, August.
- Rahimkhani, Parisa & Heydari, Mohammad Hossein, 2023. "Fractional shifted Morgan–Voyce neural networks for solving fractal-fractional pantograph differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
More about this item
Keywords
Two-dimensional variable-order fractional optimal control problem; Generalized polynomials; Operational matrix; Lagrange multipliers; Optimization method;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1389-z. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.