Citation: Huichol Choi, Kinam Sin, Sunae Pak, Kyongjin Sok, Sungryol So. Representation of solution of initial value problem for fuzzy linear multi-term fractional differential equation with continuous variable coefficient[J]. AIMS Mathematics, 2019, 4(3): 613-625. doi: 10.3934/math.2019.3.613
[1] | R. P. Agarwal, V. Lakshmikantham and J. J. Nieto, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal., 72 (2010), 2859-2862. doi: 10.1016/j.na.2009.11.029 |
[2] | S. Arshad and V. Lupulescu, On the fractional differential equations with uncertainty, Nonlinear Anal., 74 (2011), 3685-3693. doi: 10.1016/j.na.2011.02.048 |
[3] | A. Khastan, J. J. Nieto and R. Rodríiguez-López, Schauder fixed-point theorem in semilinear spaces and its application to fractional differential equations with uncertainty, Fixed Point Theory A., 2014 (2014), 21. |
[4] | T. Allahviranloo, S. Salahshour and S. Abbasbandy, Explicit solutions of fractional differential equations with uncertainty, Soft Comput., 16 (2012), 297-302. doi: 10.1007/s00500-011-0743-y |
[5] | S. Salahshour, A. Ahmadian, N. Senu, et al. On analytical solutions of the fractional differential equation with uncertainty: Application to the Basset problem, Entropy, 17 (2015), 885-902. doi: 10.3390/e17020885 |
[6] | R. Abdollahi, A. Khastan and R. Rodríguez-López, On the linear fuzzy model associated with Caputo–Fabrizio operator, Bound. Value Probl., 2018 (2018), 91. |
[7] | H. V. Ngo, V. Lupulescu and D. O'Regan, A note on initial value problems for fractional fuzzy differential equations, Fuzzy Set. Syst., 347 (2018), 54-69. doi: 10.1016/j.fss.2017.10.002 |
[8] | S. Salahshour, T. Allahviranloo and S. Abbasbandy, Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1372-1381. doi: 10.1016/j.cnsns.2011.07.005 |
[9] | M. Chehlabi and T. Allahviranloo, Concreted solutions to fuzzy linear fractional differential equations, Appl. Soft Comput., 44 (2016), 108-116. doi: 10.1016/j.asoc.2016.03.011 |
[10] | O. A. Arqub, M. AL-Smadi, S. M. Momani, et al. Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method, Soft Comput., 20 (2016), 3283-3302. doi: 10.1007/s00500-015-1707-4 |
[11] | O. A. Arqub, M. Al-Smadi, S. Momani, et al. Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems, Soft Comput., 21 (2017), 7191-7206. doi: 10.1007/s00500-016-2262-3 |
[12] | O. A. Arqub, Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations, Neural Comput. Appli., 28 (2017), 1591-1610. doi: 10.1007/s00521-015-2110-x |
[13] | M. Mazandarani and A. V. Kamyad, Modified fractional Euler method for solving fuzzy fractional initial value problem, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 12-21. doi: 10.1016/j.cnsns.2012.06.008 |
[14] | A. Ahmadian, M. Suleiman, S. Salahshour, et al. A Jacobi operational matrix for solving a fuzzy linear fractional differential equation, Adv. Differ. Equations, 2013 (2013), 104. |
[15] | A. Ahmadian, S. Salahshour and C. S. Chan, Fractional differential systems: A fuzzy solution based on operational matrix of shifted chebyshev polynomials and its applications, IEEE Trans. Fuzzy Syst., 25 (2017), 218-236. doi: 10.1109/TFUZZ.2016.2554156 |
[16] | K. Sin, M. Chen, H. Choi, et al. Fractional Jacobi operational matrix for solving fuzzy fractional differential equation, J. Intell. Fuzzy Syst., 33 (2017), 1041-1052. doi: 10.3233/JIFS-162374 |
[17] | K. Sin, M. Chen, C. Wu, et al. Application of a spectral method to fractional differential equations under uncertainty, J. Intell. Fuzzy Syst., 35 (2018), 4821-4835. doi: 10.3233/JIFS-18732 |
[18] | R. P. Agarwal, D. Baleanu, J. J. Nieto, et al. A survey on fuzzy fractional differential and optimal control nonlocal evolution equations, J. Comput. Appl. Math., 339 (2018), 3-29. doi: 10.1016/j.cam.2017.09.039 |