Parametric Analysis of a Heavy Metal Sorption Isotherm Based on Fractional Calculus

Table 1

Parameter estimation results^@.

	Parameter		𝛿𝜃𝑖	𝜃𝑖±𝑡(1−(𝛼/2)),(NE−NP)⋅𝛿𝜃𝑖; 𝜃𝑖±𝑧(1−(𝛼/2))⋅𝛿𝜃𝑖	𝑉𝜃	𝑉𝑟𝜃	𝑟	𝐹OBJ
	𝜃1	0.169	2.66⋅10^−3	0.169 ± 0.011; 0.169 ± 0.005	7.08⋅10^−6−2.02⋅10^−6−5.36⋅10^−6−2.02⋅10^−63.83⋅10^−49.37⋅10^−5−5.36⋅10^−69.37⋅10^−52.89⋅10^−5	1−0.039−0.38−0.03910.89−0.380.891	0.999	1.38⋅10^−3
EPSILON 1	𝜃2	0.884	1.96⋅10^−2	0.884 ± 0.084; 0.884 ± 0.038
	𝜃3	0.488	5.38⋅10^−3	0.488 ± 0.023; 0.488 ± 0.010
	𝜃1	0.169	3.12⋅10^−2	0.169 ± 0.134; 0.169 ± 0.061	9.74⋅10^−4−1.57⋅10^−3−1.34⋅10^−3−1.57⋅10^−33.31⋅10^−31.93⋅10^−3−1.34⋅10^−31.93⋅10^−32.05⋅10^−3	1−0.87−0.95−0.8710.74−0.950.741
EPSILON 2	𝜃2	0.884	5.76⋅10^−2	0.884 ± 0.247; 0.884 ± 0.112
	𝜃3	0.488	4.52⋅10^−2	0.488 ± 0.194; 0.488 ± 0.088

^@100 · (1 − α)% = 95%: 𝑡_{(1−(𝛼/2)),(NE−NP)}=𝑡_{0.975;(5−3)}=𝑡_0.975;2=4.3030; 𝑡_{(1−(𝛼/2)),(NE−NP)}=𝑡_{0.975;(5−2)}=𝑡_0.975;3=3.182; and 𝑡_{(1−(𝛼/2)),(∞)}=𝑧_{(1−(𝛼/2))}=𝑧_0.975=1.96.