These days, researchers are interested in the study of fuzzy differential equations. Modeling can be applied to this fuzzy differential equation to find solutions related with real-world issues. Yet, it is challenging to solve this fuzzy differential equation analytically. Thus, the purpose of this study is to present the fuzzy Runge–Kutta Cash–Karp method to solve first-order fuzzy differential equation under the interpretation of Hukuhara derivative. By applying the fuzzy Runge–Kutta Cash–Karp method, the approximate solution is obtained and compared with the analytical solution. The results indicated that the approximate solutions of the proposed method are comparable to the analytical solutions in terms of accuracy.

1.
2.
A.
Khastan
,
J. J.
Nieto
, and
R.
Rodríguez-López
,
Inf. Sci.
,
275
,
145
167
(
2014
).
3.
L. C.
Barros
,
R. C.
Bassanezi
, and
P. A.
Tonelli
,
Ecol. Modell.
,
128
,
27
33
(
2000
).
4.
A. L.
Bencsik
,
B.
Bede
,
J. K.
Tar
, and
J.
Fodor
,
Third Rom. Jt. Symp. Appl. Comput. Intell.
,
1
12
(
2006
).
5.
S. S. L.
Chang
and
L. A.
Zadeh
,
IEEE Trans. Syst. Man Cybern.
,
2
,
30
34
(
1972
).
6.
D.
Dubois
and
H.
Prade
,
Fuzzy Sets Syst.
,
8
,
225
233
(
1982
).
7.
M. L.
Puri
and
D. A.
Ralescu
,
J. Math. Anal. Appl.
,
91
,
552
558
(
1983
).
8.
O.
Kaleva
,
Fuzzy Sets Syst.
,
24
,
301
31
(
1987
).
9.
S.
Seikkala
,
Fuzzy Sets Syst.
,
24
,
319
330
(
1987
).
10.
M.
Friedman
,
M.
Ma
, and
A.
Kandel
,
Fuzzy Log. Found. Ind. Appl.
,
8
,
57
72
(
1996
).
11.
M.
Ma
,
M.
Friedman
, and
A.
Kandel
,
Fuzzy Sets Syst.
,
105
,
133
138
(
1999
).
12.
S.
Tapaswini
and
S.
Chakraverty
,
Fuzzy Inf. Eng.
,
3
,
293
312
(
2012
).
13.
A.
Georgieva
,
Mathematics
,
8
,
1
13
(
2020
).
14.
T.
Jayakumar
,
D.
Maheskumar
, and
K.
Kanagarajan
,
Appl. Math. Sci.
,
6
,
989
3002
(
2012
).
15.
A.
Ahmadian
,
S.
Salahshour
, and
C. S.
Chan
,
Soft Comput.
,
19
,
1051
1062
(
2015
).
16.
K.
Kanagarajan
and
R.
Suresh
,
Comput. Appl. Math.
,
37
,
1294
1305
(
2018
).
17.
P.
Rajkumar
and
S.
Rubanraj
,
J. Comput. Math. Sci.
,
10
,
1518
1528
(
2019
).
18.
N. Z.
Husin
,
M. Z.
Ahmad
, and
M. K. M.
Akhir
,
Mathematics
,
10
, pp.
1
25
(
2022
).
19.
R.
Goetschel
and
W.
Voxman
,
Fuzzy Sets Syst.
,
18
,
31
43
(
1986
).
This content is only available via PDF.
You do not currently have access to this content.