$t_k$

Exact solution $={\displaystyle \sum _{i=2}^n}\frac{{\left(-1\right)}^{i+1}{t}^{1.1i}}{\Gamma \left(1.1i+1\right)}$

Approximation solution $x_n\left(t\right)$

$\text{Error}=\left|x\left(t\right)-x_n\left(t\right)\right|$

0.0

0

0

0

0.1

0.073357053781371

0.058092499960337

0.015264553821034

0.2

0.151282884629052

0.135430820233760

0.015852064395293

0.3

0.226984580680193

0.211095760530730

0.015888820149463

0.4

0.29890238480688

0.283237827667134

0.015664557141554

0.5

0.366411147911488

0. 351151361983237

0.015259785928251

0.6

0.429259300754372

0.414572350125656

0.014686950628716

0.7

0.487372840288318

0.473456997040934

0.013915843247384

0.8

0.540762298480572

0.52788452424550

0.012877774238022

0.9

0.589469952960841

0.578006370352886

0.011463582607954

1

0.633536032460000

0.624016649518593

0.009519382941407