The fading is so smooth which doesn’t look like this is hand painted.
Are there any software can be used to generate this kind of texture?
Could be hand painted. You can use tools such as the Smudge Tool, Liquify or even specific directional blur in Photoshop to achieve that!
About the software: you could use Trapcode Mir or Particular to create a “ribbon” and then blur it, Flame Painter, Caustics Generator, even Krita has a brush that paints similarly to that texture, check those out!
I believe you can easily make that using this website: Flame Painter Free | online paint program
and blurring the result a bit afterwards. Have fun!
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