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Theory and Modern Applications

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