Let [X(t)]�� = [x1��(t), x2��(t)] and X0 = (1,2, 3), where [X0]�� = [1 + ��, 3 ? ��] for �� [0,1]; then the first ten +t8�¦�(8��+1)+t9�¦�(9��+1)).(45)Clearly,?????+t5�¦�(5��+1)t6�¦�(6��+1)+t7�¦�(7��+1)?????+t3�¦�(3��+1)+t4�¦�(4��+1)?????+t9�¦�(9��+1)),x2��(t)=(3?��)(1+t�¦�(��+1)+t2�¦�(2��+1)?????+t7�¦�(7��+1)+t8�¦�(8��+1)?????+t5�¦�(5��+1)+t6�¦�(6��+1)?????+t3�¦�(3��+1)+t4�¦�(4��+1)?????terms Cisplatin order of (44) can be expressed as follows:x1��(t)=(1+��)(1+t�¦�(��+1)+t2�¦�(2��+1) (45) are the valid ��-cuts of the solution of (36). For numerical approximation, we set t [0,2] and N = 100. By using Algorithm 1, the results for different values of �� are plotted in Figure 1. From the graphs, we can see that if �� approaches 1, the approximate solutions will approach the approximate solution of fuzzy differential equation.

Numerical values at t = 2 for different values of �� are listed in Table 1.Figure 1The numerical solution of (36) for (a) �� = 0.6, (b) �� = 0.8, and (c) �� = 1.Table 1Numerical solutions of Example 1 with different values of ��.Example 2 ��Consider the following linear fuzzy fractional differential equation:??cD0��X(t)=?X(t),X(0)=X0.(46)The nonfuzzy problem associated with (46) is??cD0��x(t)=?x(t),x(0)=x0.(47)In order to find the solution of (46), we first find the solution of (47). By taking the Laplace transform on both sides of (47), we have??cD0��x(t)=??x(t).(48)It follows thats��?x(t)?x(t0)s��?1=??x(t).(49)After simplifying, we get?x(t)=x0s��?1s��+1.(50)By taking the inverse Laplace transform to (50), we obtainx(t)=x0??1s��?1s��+1,(51)which finally has the following solution:x(t)=x0E��(?t��),(52)where E��() is the Mittag-Leffler function.

Using Zadeh’s extension principle to (52) in relation to x0, we obtain the solution of (46) as follows:X(t)=X0E��(?t��).(53)Let [X(t)]�� = [x1��(t), x2��(t)] and X0 = (2,3, 4) where [X0]�� = [�� + 2,4 ? ��] for �� [0,1]; then the first GSK-3 ten terms of (52) can be expressed as ?t8�¦�(8��+1)???t9�¦�(9��+1)).(54)Clearly,??????t6�¦�(6��+1)?t7�¦�(7��+1)??????t3�¦�(3��+1)?t4�¦�(4��+1)?t5�¦�(5��+1)??????t8�¦�(8��+1)?t9�¦�(9��+1)),x2��(t)=(4?��)(?1?t�¦�(��+1)?t2�¦�(2��+1)??????t6�¦�(6��+1)?t7�¦�(7��+1)??????t3�¦�(3��+1)?t4�¦�(4��+1)?t5�¦�(5��+1)?????follows:x1��(t)=(��+2)(?1?t�¦�(��+1)?t2�¦�(2��+1) (54) are the valid ��-cuts of the solution of (46). By using Algorithm 1 with the same interval t and interval N as in Example 1, the numerical solutions of (46) for different values of �� are plotted in Figure 2. Again, we can see that the numerical solutions will approach the numerical solution of fuzzy differential equation as �� increases to 1. Numerical solutions at t = 2 for different values of �� are listed in Table 2.Figure 2The numerical solutions of (46) for (a) �� = 0.