DOI QR코드

DOI QR Code

FUZZY FRACTIONAL CONFORMABLE LAPLACE TRANSFORMS

  • Received : 2021.02.25
  • Accepted : 2021.05.09
  • Published : 2021.06.25

Abstract

In this paper, we define a fractional conformable fuzzy Laplace transform and prove some related theorems. Also by using this transform we solve some fuzzy fractional differential equations.

Keywords

References

  1. A. Harir, S. Melliani and L.Chadli, Fuzzy gneralized conformable fractional derivative, Advance in Fuzzy Systems, 17(2020).
  2. A. Jafarian, A. K. Golmankhaneh and D. Baleanu, On Fuzzy fractional laplace transformation, Advances in Mathematical Physic, 385 (2014).
  3. B. Bede, SG. Gal, Generalizations of the differetiability of fuzzy-number-valued functions with applications to fuzzy differential equations,Fuzzy set syst.,(2005), 151:581-599. https://doi.org/10.1016/j.fss.2004.08.001
  4. Ch. S. Goodrich, Some new existence results for fractional difference equations, Int. J. Dynamical Syst. Diff. Eq., 3 (2011), 145-162. https://doi.org/10.1504/IJDSDE.2011.038499
  5. Ch. S. Goodrich, On discrete sequential fractional boundary value problems, J.Math.Anal.Appl., 385 (2012), 111-124. https://doi.org/10.1016/j.jmaa.2011.06.022
  6. D. Dubios, H. Prade, Towards fuzzy differential calculus,Fuzzy set syst.,(1982), 8:1-7. https://doi.org/10.1016/0165-0114(82)90025-2
  7. E. E. Olivera, J. A. T. Machado, A review of definitions for fractional derivatives and integral, Mathematics Problems in Engineering, (2014).
  8. F. M. Atici, P. W. Eloe, Discrete fractional calculus with the nabla operator, Electron. J. Qual. Theory Differ. Equ., (2009), 1-12.
  9. G. Al Nemer, M. Kenawy, M. Zakarya, C. Cesarano, H. M Rezk, Generalizations of Hardy's Type Inequalities Via Conformable Calculus. Symmetry, 13(2021),1-13. https://doi.org/10.3390/sym13010001
  10. K. B. Oldham, J. Spanier, The fractional calculus, Academic Press, New York, NY, USA,1974.
  11. ML. Puri, D. Ralescu, Differential for fuzzy function, J. Math. Anal. Appl, 91 (1983), 522-558.
  12. M. Zakarya, F. Altanji, G. AlNemer, HA. Abd El-Hamid, C. Cesarano, HM. Rezk, Fractional Reverse Coposn's Inequalities via Conformable Calculus on Time Scales, Symmetry, 13 (2021), 1-16. https://doi.org/10.3390/sym13010001
  13. R. Hilfer, Applications of fractional calculus in physics, World Scientific,2000.
  14. R. Khalil, M. Horani, A.Yousf and M. Sababheh, A new definitionof fractional derivative, J.Comput. Appl. Math., 264 (2009), 65-70.
  15. S. Liang, R. Wu and L. Chen, Laplace transform of fractional order diffrential equations, Electronic Journal of Differential Equations, 139 (2015).
  16. SSL. Chang, L. Zade, on fuzzy mapping and control, IEEE. trans syst. Cybem.(1972), 230-34.
  17. T. Abdeljawad, On conformable fractional calculus, Journal of Computional and Applied Mathematics, 279 (2015), 57-66. https://doi.org/10.1016/j.cam.2014.10.016
  18. T. Allahviranloo, M. Barkhordari, Fuzzy laplace transforms, Soft comput., 14 (2010), 235-243. https://doi.org/10.1007/s00500-008-0397-6
  19. Z. AL-zhour, F. Alrawajeh, N. AL-mutairi and R. Alkhasawnef, New results on the conformable fractional sumudu transform, International Journal of Analysis and Applications, 17(2019),6, 1019-1033.