Figures caption
Figure 1. 3D plots of the solution \(Q_{1}(x,y=1,t)\),
obtained by the gKM: (a) real part, (b) imaginary part, (c) modulus, and
(d)-(f): the cross sectional 2D line plots of (a)-(c) at \(t=0\),
respectively, for the particular choice of the free parameters\(p=1\), \(q=1\), \(h_{1}=2\), \(h_{2}=1\), \(l_{1}=1\),\(l_{2}=2\), \(d=1\), \(a=3.5\), \(b_{1}=1\) and\(\theta_{0}=0\).
Figure 2. 3D plots of the solution \(Q_{3}(x,y=1,t)\),
obtained by the gKM: (a) real part, (b) imaginary part, (c) modulus, and
(d)-(f): the cross sectional 2D line plots of (a)-(c) at \(t=0\),
respectively, with \(p=1\), \(q=1\), \(h_{1}=2\), \(h_{2}=1\),\(l_{1}=1\), \(l_{2}=2\), \(d=1\), \(a=3.5\), \(b_{1}=1\) and\(\theta_{0}=0\).
Figure 3 . 3D plots of the solution \(Q_{1}(x,y=1,t)\),
obtained by the NAEM: (a) real part, (b) imaginary part, (c) modulus,
and (d)-(f): the cross sectional 2D line plots of (a)-(c) at \(t=0\),
respectively, with \(\alpha=1\), \(\beta=1\), \(\sigma=1\),\(p=1\), \(q=1\), \(h_{1}=2\), \(h_{2}=1\), \(l_{1}=1\),\(l_{2}=2\), and \(\theta_{0}=0\).
Figure 4 . 3D plots of the solution \(Q_{5}(x,y=1,t)\),
obtained by the NAEM: (a) real part, (b) imaginary part, (c) modulus,
and (d)-(f): the cross sectional 2D line plots of (a)-(c) at \(t=0\),
respectively, with\(\ \alpha=1\), \(\beta=3\), \(\sigma=1\),\(p=1\), \(q=1\), \(h_{1}=2\), \(h_{2}=1\), \(l_{1}=1\),\(l_{2}=2\), and \(\theta_{0}=0\).
Figure 5. 3D plots of the solution \(Q_{7}(x,y=1,t)\),
obtained by the NAEM: (a) real part, (b) imaginary part, (c) modulus,
and (d)-(f): the cross sectional 2D line plots of (a)-(c) at \(t=0\),
respectively, with 7\(\alpha=1\), \(\beta=3\), \(\sigma=1\),\(p=1\), \(q=1\), \(h_{1}=2\), \(h_{2}=1\), \(l_{1}=1\),\(l_{2}=2\), and \(\theta_{0}=0\).
Figure 6. Effects of the fractional parameter on\(\left|Q_{1}(x,y=1,t;\tau,\theta=45)\ \right|\), obtained by
the gKM: (a)-(d) with \(\tau=0.25,\ \ 0.50,\ \ 0.75,\ \ 1\),
respectively, for the particular choice of the free parameters\(p=1\), \(q=1\),\(\ \theta=45\), \(d=1\), \(k=1\),\(a=3.5\),\(\ b_{1}=1\) and \(\theta_{0}=0\), and the cross
sectional 2D line plots of (a)-(d): (e) variation of the surface profile
along \(x\)-axis at \(t=2\) and (f) variation of the surface profile
along \(t\)-axis at \(x=1\).
Figure 7. Effects of wave obliqueness on\(\left|Q_{1}(x,y=1,t;\tau=0.75,\theta)\ \right|\), obtained by
the gKM: (a)-(h) of\(\theta=15,\ 30{,\ 45},\ 75,105,\ 120{,\ 135},\ 165\),
respectively, with \(p=1\), \(q=1\),\(\ \tau=0.75\),\(d=1\),\(\ k=1\), \(a=3.5\), \(b_{1}=1\), and\(\theta_{0}=0\), and the cross sectional 2D line plots of (a)-(h):
(i) variation of the surface profile along \(x\)-axis at \(t=2\) and
(j) variation of the surface profile along \(t\)-axis at \(x=1\).
Figure 8 . Effects of wave obliqueness on\(\left|Q_{1}(x=1,y=1,t;\tau=0.75,\theta)\right|\), obtained by
the gKM: (a) 3D plot and (b) variation of the surface profile along\(t\)-axis with respect to different oblique wave directions. Effects of
the fractional parameter on the solution\(\left|Q_{1}(x=1,y=1,t=2;\tau,\theta)\right|\), obtained by the
gKM: (c) 3D plot and (d) variation of the surface profile along oblique
wave direction with respect to different fractional values.
Figure 9 . Effects of the fractional parameter on\(\left|Q_{1}(x,y=1,t;\tau,\theta=45)\right|\), obtained by the
NAEM: (a)-(d) of \(\tau=0.25,\ \ 0.5,\ \ 0.75,\ \ 1\), respectively,
for the particular choice of the free parameters \(\alpha=1\),\(\beta=1\), \(\sigma=1\), \(p=1\),\(q=1\),\(\ k=1,\ \theta=45\)and \(\theta_{0}=0\), and the
cross sectional 2D line plots of (a)-(d): (e) variation of the surface
profile along \(x\)-axis at \(t=2\) and (f) variation of the surface
along \(t\)-axis at \(x=1\).
Figure 10 . Effects of wave obliqueness on\(\left|Q_{1}(x,y=1,t;\tau=0.75,\theta)\right|\), obtained by the
NAEM: (a)-(h) of\(\theta=15,\ 30{,\ 45},\ 75,105,\ 120{,\ 135},\ 165\),
respectively, with \(\alpha=1\), \(\beta=1\), \(\sigma=1\),\(p=1\), \(q=1\), \(k=1,\ \tau=0.75\ \)and \(\theta_{0}=0\),
and the cross sectional 2D line plots of (a)-(h): (i) variation of the
surface profile along \(x\)-axis at \(t=2\) and (j) variation of the
surface profile along \(t\)-axis at \(x=1\).