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Table 3 Comparison of exact and approximate solution of Example  3 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 ) N  = 2 N  = 3 N  = 4 N  = 5 N  = 6
t = 0.0 1.000000000 1.0152591045 0.9989268650 1.0000584609 0.9999973751 1.000000102
t = 0.1 1.105170918 1.1048778054 1.1055690936 1.1051373901 1.1051724714 1.105170872
t = 0.2 1.221402758 1.2115236915 1.2222416889 1.2213694032 1.2214034018 1.221402755
t = 0.3 1.3498588075 1.3351967629 1.3506284171 1.3498396744 1.3498594914 1.349858762
t = 0.4 1.4918246976 1.4758970196 1.4924130441 1.4918009400 1.4918267043 1.491824610
t = 0.5 1.6487212707 1.6336244616 1.6492793361 1.6486734983 1.6487243484 1.648721203
t = 0.6 1.8221188003 1.8083790888 1.8229110590 1.8220452095 1.8221217781 1.822118764
t = 0.7 2.0137527074 2.0001609012 2.0149919788 2.0136714962 2.0137550986 2.013752651
t = 0.8 2.2255409284 2.2089698990 2.2272058616 2.2254753425 2.2255438696 2.225540838
t = 0.9 2.4596031111 2.4348060820 2.4612364735 2.4595472949 2.4596078085 2.459603059
t = 1.0 2.7182818284 2.6776694503 2.7187675805 2.7181454617 2.7182834949 2.718281628