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Table 1 Numerical illustration for the q-HATM solution of FEFK equation defined in Case 2 for distinctα at \(n=1\), \(\hslash=1\) and \(y=0.1\)

From: Analytical approach for fractional extended Fisher–Kolmogorov equation with Mittag-Leffler kernel

x t α = 0.7 α = 0.8 α = 0.9 α = 1
0.25 0.025 1.40637 × 10−3 6.71262 × 10−4 2.62076 × 10−4 2.37588 × 10−5
0.050 2.07408 × 10−3 9.74998 × 10−4 3.96960 × 10−4 4.46453 × 10−5
0.075 2.57439 × 10−3 1.17156 × 10−3 4.89850 × 10−4 6.18806 × 10−5
0.1 2.98624 × 10−3 1.30695 × 10−3 5.58417 × 10−4 7.48574 × 10−5
0.50 0.025 2.72578 × 10−3 1.30527 × 10−3 5.09260 × 10−4 4.57329 × 10−5
0.050 4.02071 × 10−3 1.92679 × 10−3 7.86281 × 10−4 7.89672 × 10−5
0.075 4.99163 × 10−3 2.38024 × 10−3 1.00472 × 10−3 9.24355 × 10−5
0.1 5.79138 × 10−3 2.76164 × 10−3 1.20515 × 10−3 8.00485 × 10−5
0.75 0.025 3.87642 × 10−3 1.86469 × 10−3 7.26833 × 10−4 6.44136 × 10−5
0.050 5.71957 × 10−3 2.81353 × 10−3 1.15165 × 10−3 9.73346 × 10−5
0.075 7.10277 × 10−3 3.60183 × 10−3 1.53830 × 10−3 7.70330 × 10−5
0.1 8.24315 × 10−3 4.37972 × 10−3 1.95701 × 10−3 1.48722 × 10−5
1 0.025 4.78660 × 10−3 2.31329 × 10−3 9.00816 × 10−4 7.87386 × 10−5
0.050 7.06455 × 10−3 3.56805 × 10−3 1.46487 × 10−3 1.01035 × 10−4
0.075 8.77561 × 10−3 4.72501 × 10−3 2.03957 × 10−3 2.54775 × 10−5
0.1 1.01876 × 10−2 5.98686 × 10−3 2.72760 × 10−3 1.83073 × 10−4