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Theory and Modern Applications

Table 3 Comparison of the numerical solutions with the other methods for \(\pmb{\alpha=3/4}\) of Example 2

From: Numerical solution of fractional-order Riccati differential equation by differential quadrature method based on Chebyshev polynomials

x

Present method N  = 8

Method in [ 19 ] k  = 6, m  = 2

Method in [ 21 ]

0.1

0.185553

0.190108

0.178692

0.2

0.305933

0.309886

0.301614

0.3

0.400771

0.404552

0.397897

0.4

0.478985

0.481638

0.476155

0.5

0.543038

0.545178

0.540568

0.6

0.595789

0.597790

0.594017

0.7

0.640095

0.641801

0.638671

0.8

0.677553

0.678835

0.676201

0.9

0.709031

0.710182

0.707923

1.0

0.735843

 

0.734913