Solution of Some Types for Composition Fractional Order Differential Equations Corresponding to Optimal Control Problems

Table 1

The values of Caputo fractional derivative when (, and in Case 1) and ( in Case 2 needed later on) are shown.

1	0	1	0	0	0.6722	0.6274	0	0.8154
1	1	1	0	0	0	0	0	0
1	2	1	0	0	0.0387	0.0287	0	0.0572
2	0	1	0.6722	0.6274	-0.6722	-0.6274	0.8154	-0.8154
2	1	1	0	0	0	0	0	0
2	2	1	0.0387	0.0287	-0.0387	-0.0287	0.0572	-0.0572
2	0	2	-0.5777	-0.5210	0.5777	0.5210	-0.7720	0.7720
2	1	2	0	0	0	0	0	0
2	2	2	0.0592	0.0620	-0.0592	-0.0620	0.0396	-0.0396
			0.1924	0.1971	0.5185	0.459	0.1402	0.7324
			0.3848	0.3942	0.5185	0.459	0.2804	0.7324