不确定分数阶Bagley-Torvik方程的解
Solving the Fractional Bagley-Torvik Equations with Uncertainty
摘要: 本文研究分数阶Bagley-Torvik方程不确定边值条件下的解。基于Caputo分数阶导数定义和广义的Hukuhara可微性，引进模糊Laplace变换，不确定边界条件为模糊数，给出了问题的级数解。数值结果分析了解的性态。
Abstract: This paper investigates the problem of the fractional Bagley-Torvik equation with uncertainty boundary-value conditions. Under the Caputo’s H-differentiability, the fuzzy Laplace transform is introduced. The uncertainty boundary-value conditions are assumed to be fuzzy numbers. The se-ries solution of fractional Bagley-Torvik equation is given. Numerical results are shown to illustrate the obtained solution.
文章引用：刘雪铃, 廖珊莉, 吴远波, 钟献词. 不确定分数阶Bagley-Torvik方程的解[J]. 应用数学进展, 2018, 7(1): 39-46. https://doi.org/10.12677/AAM.2018.71006

参考文献

[1] Salahshour, S., Allahviranloo, T., Abbasbandy, S. and Baleanu, D. (2012) Existence and Uniqueness Results for Fractional Differential Equations with Uncertainty. Advances in Difference Equations, 2012, 1-12.
[Google Scholar] [CrossRef] 
[2] Chalco-Cano, Y. and Román-Flores, H. (2008) On New Solutions of Fuzzy Differential Equations. Chaos Solitons & Fractals, 38, 112-119.
[Google Scholar] [CrossRef] 
[3] Wu, H.C. (1998) The Fuzzy Riemann Integral and Its Numerical Integration. Information Sciences, 111, 109-137.
[Google Scholar] [CrossRef] 
[4] Agarwal, R.P., Lakshmikantham, V. and Nieto, J.J. (2010) On the Con-cept of Solution for Fractional Differential Equations with Uncertainty. Nonlinear Analysis Theory Methods & Applications, 72, 2859-2862.
[Google Scholar] [CrossRef] 
[5] Salahshour, S., Allahviranloo, T. and Abbasbandy, S. (2012) Solving Fuzzy Fractional Differential Equations by Fuzzy Laplace Transforms. Communications in Nonlinear Science & Numerical Simulation, 17, 1372-1381.
[Google Scholar] [CrossRef] 
[6] Salahshour, S. and Haghi, E. (2010) Solving Fuzzy Heat Equation by Fuzzy Laplace Transforms. Communications in Computer Information Science, 81, 512-521.
[Google Scholar] [CrossRef] 
[7] Mazandarani, M. and Kamyad, A.V. (2013) Modified Fractional Euler Method for Solving Fuzzy Fractional Initial Value Problem. Communications in Nonlinear Science Numerical Simulation, 18, 12-21.
[Google Scholar] [CrossRef] 
[8] Allahviranloo, T. and Ahmadi, M.B. (2010) Fuzzy Laplace Transforms. Soft Computing, 14, 235-243.
[Google Scholar] [CrossRef] 
[9] Khodadadi, E. and Karabacak, M. (2015) Solving Fuzzy Fractional Partial Differential Equations by Fuzzy Laplace-Fourier Transforms. Journal of Computational Analysis & Applications, 19, 260-271.
[10] Buckley, J.J., Eslami, E. and Feuring, T. (2002) Solving Fuzzy Equations. Fuzzy Sets & Systems, 50, 1-14.
[Google Scholar] [CrossRef] 
[11] Bede, B., Rudas, I.J. and Bencsik, A.L. (2007) First Order Linear Fuzzy Differential Equations under Generalized Differentiability. Information Sciences, 177, 1648-1662.
[Google Scholar] [CrossRef] 
[12] Allahviranloo, T. and Ahmadi, M.B. (2010) Fuzzy Laplace Transforms. Soft Computing, 14, 235-243.
[Google Scholar] [CrossRef] 
[13] Torvik, P.J. and Bagley, R.L. (1984) On the Appearance of the Fractional Derivative in the Behavior of Real Materials. Journal of Applied Mechanics, 51, 294-298.
[Google Scholar] [CrossRef] 
[14] Salahshour, S., Ahmadian, A. and Chan, C.S. (2016) A Novel Technique for Solving Fuzzy Differential Equations of Fractional Order Using Laplace and Integral Transforms. IEEE International Conference on Fuzzy Systems, 2016, 1473-1477.
[15] Goetschel, R. and Voxman, W. (1986) Elementary Fuzzy Calculus. Fuzzy Sets and Systems, 18, 31-43.
[16] Goetschel, R. and Voxman, W. (1985) Eigen Fuzzy Number Sets. Fuzzy Sets and Systems, 16, 75-85.
[Google Scholar] [CrossRef] 
[17] Chang, S.S.L. and Zadeh, L.A. (1972) On Fuzzy Mapping and Control. IEEE Transactions on Systems Man & Cybernetics, 2, 30-34.
[Google Scholar] [CrossRef] 
[18] Kaleva, O. (1987) Fuzzy Differential Equations. Fuzzy Sets & Systems, 24, 301-317.
[Google Scholar] [CrossRef] 
[19] Seikkala, S. (1987) On the Fuzzy Initial Value Problem. Fuzzy Sets & Systems, 24, 319-330.
[Google Scholar] [CrossRef] 
[20] Salahshour, S. and Allahviranloo, T. (2013) Applications of Fuzzy Laplace Transforms. Soft Computing, 17, 145-158.
[Google Scholar] [CrossRef] 

为你推荐