Table 1.
Maximum absolute error comparison between conformable-Caputo FNPSM and finite difference/collocation method (FDCM) [38] for Example 1, where x ∈ [0, 1].
Table 2.
Error norm comparison between conformable-Caputo FNPSM and exact solution for Example 1, where x ∈ [0, 1] and α = 0.5.
Fig 1.
Curve of exact and conformable-Caputo FNPS solutions for Example 1, where x ∈ [0, 1], t = 0.2 and α = 0.5.
Fig 2.
3D mesh plot of numerical solution for Example 1, where x ∈ [0, 1]t ∈ [0, 1] and α = 0.75.
Fig 3.
Fractional order α effect on u(x, t) for Example 1, where 0 ≤ x ≤ 1 and t = 0.2.
Fig 4.
Time different value effect on u(x, t) for Example 1, where α = 0.25 and 0 ≤ x ≤ 1.
Fig 5.
Curve of exact and conformable-Caputo FNPS solutions for Example 2, where x ∈ [0, 1], t = 0.2 and α = 0.5.
Fig 6.
3D mesh plot of numerical solution for Example 2, where x ∈ [0, 1]t ∈ [0, 1] and α = 0.75.
Fig 7.
Time different value effect on u(x, t) for Example 2, where α = 0.25 and 0 ≤ x ≤ 1.
Table 3.
Error norm comparison between Caputo FNPSM and conformable FNPSM for Example 2, where x ∈ [0, 1] and α = 0.5.