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Table 4 Comparison of exact and approximate solution of Example  4 using the boundary condition as defined in \(\pmb{\mathbf{S_{2}}}\)

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

t N
  Exact U ( t ) First iteration Second iteration Third iteration Fourth iteration
t = 0.0 1.0000000000 0.9993612934 1.0001381646 1.0000260271 1.000000020
t = 0.1 1.0168063300 1.1131408265 1.0322239559 1.0171510593 1.016806465
t = 0.2 1.0338951135 1.2060058045 1.0595571295 1.0344373486 1.033895324
t = 0.3 1.0512710963 1.2803801650 1.0835040499 1.0519291558 1.051271352
t = 0.4 1.0689391057 1.3388134647 1.1052061945 1.0696628704 1.068939387
t = 0.5 1.0869040495 1.3839808784 1.1255801546 1.0876670104 1.086904346
t = 0.6 1.1051709180 1.4186831997 1.1453176345 1.1059622221 1.105171226
t = 0.7 1.1237447856 1.4458468410 1.1648854519 1.1245612803 1.123745105
t = 0.8 1.1426308117 1.4685238330 1.1845255377 1.1434690886 1.142631142
t = 0.9 1.1618342427 1.4898918253 1.2042549363 1.1626826787 1.161834578
t = 1.0 1.1813604128 1.5132540859 1.2238658054 1.1821912111 1.181360731