A reliable method for the space-time fractional Burgers and time-fractional Cahn-Allen equations via the FRDTM

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 The results obtained by the FRDTM for different values of β for Example 4.2

x	t	β = 0.25	β = 0.5	β = 0.75	β = 1
x	t	Numerical	Numerical	Numerical	Numerical	Exact
0.1	2	−0.0764845	−0.0764173	−0.0765568	−0.076893	−0.073117
	3	−0.0224361	−0.0224164	−0.0224575	−0.0225564	−0.0214477
	4	−0.00609528	−0.00608992	−0.00610107	−0.00612793	−0.00582667
	6	0.00309842	0.00309573	0.00310145	0.00311518	0.00296201
0.3	2	−0.243822	−0.24332	−0.244843	−0.248451	−0.21341
	3	−0.0721999	−0.0720561	−0.0725197	−0.0736135	−0.0631537
	4	−0.0195606	−0.019521	−0.0196462	−0.019942	−0.0171018
	6	0.0102373	0.0102193	0.0102888	0.0104509	0.008961
0.5	2	−0.419375	−0.418177	−0.4228	−0.433774	−0.336983
	3	−0.126549	−0.126227	−0.127726	−0.131255	−0.101393
	4	−0.034099	−0.0340076	−0.0344084	−0.0353558	−0.0272609
	6	0.0188912	0.0188622	0.0191169	0.0197044	0.0151832
0.6	2	−0.505904	−0.504266	−0.511001	−0.527077	−0.389893
	3	−0.154611	−0.154193	−0.156467	−0.161845	−0.118574
	4	−0.0414992	−0.041377	−0.0419815	−0.0434176	−0.0317049
	6	0.0238959	0.0238714	0.0242898	0.0252544	0.0184231