Keywords:-
Article Content:-
Abstract
It is essential to use fuzzy differential equations in order to simulate a wide range of physical, applied, and engineering phenomena and uncertainties. For some fuzzy differential equations, obtaining precise solutions is quite challenging, hence reliable and effective analytical methods are essential. These fuzzy fractional differential equations will be studied in this research. Conformable fractional differentiability is examined in this paper, with the goal of developing an existence and uniqueness thesis for a fuzzy fractional differential equation using the idea of conformable differentiability, which is based on expanding a fuzzy mapping's class of differentiable fuzzy mappings. For this, we consider lateral Hukuhara derivatives of order q ∈ (0, 1).
References:-
References
2. Z. Shuqin, “Monotone iterative method for initial value problem involving Reimann Liouville fractional derivatives,” Nonlinear Analysis, vol. 71, pp. 2087–2093, 2009.
3. G. Gumah, M. F. M. Naser, M. Al-Smadi, S. K. Q. Al-Omari, and D. Baleanu, “Numerical solutions of hybrid fuzzy differential equations in a Hilbert space,” Applied Numerical Mathematics, vol. 151, pp. 402–412, 2020.
4. O. A. Arqub and M. Al-Smadi, “Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions,” Soft Computing, vol. 24, no. 16, pp. 12501–12522, 2020.
5. L. Stefanini, “A generalization of Hukuhara difference and division for interval and fuzzy arithmetic,” Fuzzy Sets and Systems, vol. 161, no. 11, pp. 1564–1584, 2010.
6. G. A. Anastassiou and S. G. Gal, “On a fuzzy trigonometric approximation theorem of weierstrasstype,” Journal of Fuzzy Mathematics, vol. 9, pp. 701–708, 2001.
7. Atangana, On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation, Appl Math Comput (2016)
8. O. Abu Arqub et al., Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense, Chaos, Solitons Fractals (2019)
9. N.V. Hoa et al., Fuzzy fractional differential equations under Caputo-Katugampola fractional derivative approach Fuzzy Sets Syst (2019)
10. T. Allahviranloo et al., On the fuzzy fractional differential equation with interval Atangana-Baleanu fractional derivative approach,Chaos, Solitons Fractals (2020)