Solving Famous Nonlinear Coupled Equations with Parameters Derivative by Homotopy Analysis Method

<table>Explicit numerical solutions with <svg height="10.95" id="M145" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 47.049999 10.95" width="47.049999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.95)">
<g transform="translate(72,-63.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="10.677562" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="31.282507" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.9125" id="M146" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 48.299999 10.9125" width="48.299999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
<tspan style="font-size: 12.50px; " x="10.515023" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.555412" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="28.806911" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="32.282745" y="0">4</tspan>
</text>
</g>
</g>
</svg>, <svg height="13.6625" id="M147" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 75.987503 13.6625" width="75.987503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.6625)">
<g transform="translate(72,-61.07)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">a</tspan>
<tspan style="font-size: 12.50px; " x="5.551332" y="0">n</tspan>
<tspan style="font-size: 12.50px; " x="11.802832" y="0">d</tspan>
<tspan style="font-size: 12.50px; " x="22.217831" y="0">𝛽</tspan>
<tspan style="font-size: 12.50px; " x="32.670338" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="44.698223" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="50.949726" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="54.42556" y="0">3</tspan>
</text>
</g>
</g>
</svg>.</table>

International Journal of Differential Equations

fig3

Figure 3

Figure 3: Solving Famous Nonlinear Coupled Equations with Parameters Derivative by Homotopy Analysis Method 