Analysis of differential equations involving Caputo–Fabrizio fractional operator and its applications to reaction–diffusion equations

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Numerical comparison between approximate solutions \(u_{\mathrm{ILTM}}\), \(u_{\mathrm{RPSM}}\), \(u_{\mathrm{FVIM}}\) and exact solution of (23) for \(x=0.01\), \(\theta =0.8\)

t	γ = 0.8			γ = 1		Absolute error
t	\(u_{\mathrm{ILTM}}\)	\(u_{\mathrm{RPSM}}\)	\(u_{\mathrm{FVIM}}\)	\(u_{\mathrm{ILTM}}\)	\(u_{\mathrm{RPSM}}\)	\(\|u_{\mathrm{exact}}-u_{\mathrm{ILTM}}\|\) for γ = 1
0.01	0.486180	0.499745	0.499774	0.501018	0.501018	2.97766 × 10⁻⁴
0.05	0.483787	0.494437	0.494541	0.498018	0.498018	5.80223 × 10⁻⁴
0.10	0.480798	0.489004	0.489186	0.494268	0.494268	1.67898 × 10⁻³
0.15	0.477812	0.484113	0.484366	0.490519	0.490518	2.77608 × 10⁻³
0.20	0.474829	0.479543	0.479864	0.486771	0.486769	3.87305 × 10⁻³