
AIMS Mathematics, 2019, 4(3): 613625. doi: 10.3934/math.2019.3.613
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Representation of solution of initial value problem for fuzzy linear multiterm fractional differential equation with continuous variable coefficient
1 Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea
2 Information Technology Institute, University of Sciences, Pyongyang, Democratic People’s Republic of Korea
3 Institute of Advanced Science, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea
Received: , Accepted: , Published:
Special Issues: New trends of numerical and analytical methods with application to real world models for instance RLC with new nonlocal operators
References
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), 28592862.
2. S. Arshad and V. Lupulescu, On the fractional differential equations with uncertainty, Nonlinear Anal., 74 (2011), 36853693.
3. A. Khastan, J. J. Nieto and R. RodríiguezLópez, Schauder fixedpoint 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), 297302.
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), 885902.
6. R. Abdollahi, A. Khastan and R. RodríguezLópez, 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), 5469.
8.S. Salahshour, T. Allahviranloo and S. Abbasbandy, Solving fuzzy fractional differential equations by fuzzy Laplace transforms, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 13721381.
9. M. Chehlabi and T. Allahviranloo, Concreted solutions to fuzzy linear fractional differential equations, Appl. Soft Comput., 44 (2016), 108116.
10. O. A. Arqub, M. ALSmadi, S. M. Momani, et al. Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method, Soft Comput., 20 (2016), 32833302.
11. O. A. Arqub, M. AlSmadi, S. Momani, et al. Application of reproducing kernel algorithm for solving secondorder, twopoint fuzzy boundary value problems, Soft Comput., 21 (2017), 71917206.
12. O. A. Arqub, Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations, Neural Comput. Appli., 28 (2017), 15911610.
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), 1221.
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), 218236.
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), 10411052.
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), 48214835.
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), 329.
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)