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Table 1 Comparison of exact and approximate solution of Example  1 using the boundary condition as defined in \(\pmb{\mathbf{S_{1}}}\)

From: Approximate solution of linear and nonlinear fractional differential equations under m-point local and nonlocal boundary conditions

t N
  Exact U ( t ) N  = 5 N  = 7 N  = 9 N  = 11
t = 0.4 0.95105651629 0.9677391807 0.9499276887 0.9510565133 0.95105651554
t = 0.8 0.58778525229 0.5806739865 0.5877691649 0.5877785192 0.5877882463
t = 1.2 −0.58778525229 −0.5879798137 −0.5877896195 −0.5877852801 −0.58778528235
t = 1.6 −0.95105651629 −0.9318025727 −0.9510687377 −0.9510565637 −0.9510565256
t = 2.0 −0.00000000000 −0.0160927142 −0.0000151536 −0.0000001456 −0.00000000975
t = 2.4 0.95105651629 0.9684572120 0.9510519403 0.9510565108 0.95105651183
t = 2.8 0.58778525229 0.5667990904 0.5879771600 0.5877852533 0.5877852523
t = 3 0.00000000000 0.0634719308 −0.0001774663 0.0000000045 0.00000000125