Have a personal or library account? Click to login
A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation Cover

A Neural Computational Intelligence Method Based on Legendre Polynomials for Fuzzy Fractional Order Differential Equation

Open Access
|Dec 2016

References

  1. [1] Z. Li, D. Chen, J. Zhu, and Y. Liu, Nonlinear dynamics of fractional order Duffing system, Chaos, Solitons & Fractals, 81 (2015) 111–116.
  2. [2] S. Pourdehi, A. Azami, and F. Shabaninia, Fuzzy Kalman-type filter for interval fractional-order systems with finite-step auto-correlated process noises, Neurocomputing, 159 (2015) 44–49.
  3. [3] A. Boulkroune, A. Bouzeriba, and T. Bouden, Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems, Neurocomputing, 173(3) (2016) 606-614.10.1016/j.neucom.2015.08.003
  4. [4] Y. Ji, L. Su, and J. Qiu, Design of fuzzy output feedback stabilization for uncertain fractional-order systems, Neurocomputing, 173(3) (2016) 1683-1693.10.1016/j.neucom.2015.09.041
  5. [5] Y. Zheng, Fuzzy prediction-based feedback control of fractional order chaotic systems, Opt. - Int. J. Light Electron Opt., 126(24) (2015) 5645-5649.10.1016/j.ijleo.2015.08.164
  6. [6] S. T. S. Chakraverty, A New Approach to Fuzzy Initial Value Problem by Improved Euler Method, Fuzzy information and Engineering, 4(3) (2012) 293–312.10.1007/s12543-012-0117-x
  7. [7] V. H. Ngo, Fuzzy fractional functional integral and differential equations, Fuzzy Sets Syst., 280 (2015) 58–90.
  8. [8] N. Van Hoa, Fuzzy fractional functional differential equations under Caputo gH-differentiability, Commun. Nonlinear Sci. Numer. Simul., 22 (2015) 1134–1157.
  9. [9] T. Senthilkumar, Robust stabilization and H ∞ control for nonlinear stochastic T–S fuzzy Markovian jump systems with mixed time-varying delays and linear fractional uncertainties, Neurocomputing, 173(3) (2016) 1615–1624.10.1016/j.neucom.2015.09.033
  10. [10] H. Delavari, R. Ghaderi, A. Ranjbar, and S. Momani, Fuzzy fractional order sliding mode controller for nonlinear systems, Commun. Nonlinear Sci. Numer. Simul., 15(4) (2010) 963–978.10.1016/j.cnsns.2009.05.025
  11. [11] S. Salahshour, T. Allahviranloo, and S. Abbasbandy, Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun. Nonlinear Sci. Numer. Simul., 17(3) (2012) 1372–1381.10.1016/j.cnsns.2011.07.005
  12. [12] S. Tapaswini, S. Chakraverty, and D. Behera, Numerical solution of the imprecisely defined inverse heat conduction problem, Chin. Phys. B, 24(5) (2015) 05020310.1088/1674-1056/24/5/050203
  13. [13] A. Ahmadian, M. Suleiman, and S. Salahshour, An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional-Order Differential Equations, Abstract and appl. analysis, 2013 Article ID 50590310.1155/2013/505903
  14. [14] T. Allahviranloo,, N. Ahmady, and E. Ahmady, Numerical solution of fuzzy differential equations by predictor–corrector method, Information Sciences, 177(7) (2007) 1633-1647.10.1016/j.ins.2006.09.015
  15. [15] M.Z. Ahmad, M.K. Hasan, and B.D. Baets, Analytical and numerical solutions of fuzzy differential equations, Information Sciences, 236 (2013) 156–167.
  16. [16] A. Khastan, and K. Ivaz, Numerical solution of fuzzy differential equations by Nyström method, Chaos, Solitons & Fractals, 41(2) (2009) 859–868.10.1016/j.chaos.2008.04.012
  17. [17] E. ElJaoui, S. Melliani, and L.S. Chadli, Solving second-order fuzzy differential equations by the fuzzy Laplace transform method, Advances in diff. Eqn., (2015) 2015: 66.10.1186/s13662-015-0414-x
  18. [18] N. A. Khan, F. Riaz, and O. A. Razzaq, A comparison between numerical methods for solving fuzzy fractional differential equations, Non Linear Engineering, 3(3) (2014) 155-162.10.1515/nleng-2013-0029
  19. [19] N. A. Khan, , O. A. Razzaq, and F. Riaz, Numerical Simulations for Solving Fuzzy Fractional Differential Equations by Max-Min Improved Euler Methods, JACSM, 7(1) (2015) 53-83.10.1515/jacsm-2015-0010
  20. [20] H. Sadoghi, M. Pakdaman, and H. Modaghegh, Unsupervised kernel least mean square algorithm for solving ordinary differential equations, Neurocomputing, 74(12-13) (2011) 2062–2071.10.1016/j.neucom.2010.12.026
  21. [21] S. Mall and S. Chakraverty, Numerical solution of nonlinear singular initial value problems of Emden – Fowler type using Chebyshev Neural Network method, Neurocomputing, 149 (2015) 975–982.
  22. [22] A. J. Meade, The Numerical Solution of Linear Ordinary Differential Equations by Feedforward Neural Networks, 19(12) (1994) 1-25.10.1016/0895-7177(94)90095-7
  23. [23] A. J. Meade and A. A. Fernandez, Solution of Nonlinear Ordinary Differential Equations by Feedforward Neural Networks, Math.Comp.Model., 20(9) (1994) 19–44.10.1016/0895-7177(94)00160-X
  24. [24] I. E. Lagaris, A. C. Likas, and D. I. Fotiadis, Artifical Neural Networks for Solving Ordinary and Partial Differential Equations, Neural Networks, IEEE Trans., 9(5) (1998) 1–26.10.1109/72.71217818255782
  25. [25] I. E. Lagaris, A. C. Likas, and D. G. Papageorgiou, Neural-Network Methods for Boundary Value Problems with Irregular Boundaries, 11(5) (2000) 1041–1049.10.1109/72.87003718249832
  26. [26] D. R. Parisi, C. Mariani, and M. A. Laborde, Solving differential equations with unsupervised neural networks, Chem. Eng. Process. Process Intensif., 42 (2003) 715–721.
  27. [27] A. Malek and R. S. Beidokhti, Numerical solution for high order differential equations using a hybrid neural network - Optimization method, Appl. Math. Comput., 183 (2006) 260–271.
  28. [28] H. J. Zimmermann, Fuzzy set theory and its application, Dordrecht, Kluwer Academi Publishers, 1991.10.1007/978-94-015-7949-0
  29. [29] D. Dubois, and H. Prade, Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, USA, 2000.10.1007/978-1-4615-4429-6
  30. [30] B.R. Sontakke and A.S. Shaikh, Properties of Caputo operator and its applications to linear fractional differential equations, International Journal of Engineering Research and Applications, 5(5) (2015) 22-29.
  31. [31] M. Caputo, Linear models of dissipation whose Q is almost frequency independent-II, Geophysical Journal International, 13(5) (1967) 529-56810.1111/j.1365-246X.1967.tb02303.x
  32. [32] S. Salahshour, T. Allahviranloo, and S. Abbasbandy, Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun Nonlinear Sci Numer Simulat, 17 (2012) 1372–1381.
  33. [33] G. J. Klir, and B. Yuan, FUZZY SETS AND FUZZY LOGIC Theory and Applications, Prentice Hall P T R Upper Saddle River, New Jersey 07458
  34. [34] D. Dubois, and H. Prade, Operations on fuzzy numbers, INT. J. SYSTEMS SCI., 9(6) (1978) 613-626.10.1080/00207727808941724
  35. [35] S. Ledesma, G. Aviña, and R. Sanchez, Practical considerations for simulated annealing implementation, In: Tan CM, editor. Simulated Annealing, InTech, 2008.10.5772/5560
DOI: https://doi.org/10.1515/jamsi-2016-0009 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180
Language: English
Page range: 67 - 82
Published on: Dec 30, 2016
Published by: University of Ss. Cyril and Methodius in Trnava
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2016 N. A. Khan, A. Shaikh, M. A. Zahoor Raja, S. Khan, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.