I went through this first paper.
I start with the source. A mathematics journal. Not biology, chemistry, or meteorology or related field.
I look at who referenced it. Not many. Referenced several times by the primary author, in papers not related to climate change.
I look for justification for the claim that a six degree rise will lead to phytoplankton death. I don't see any. Searching google scholar briefily, I don't find any support. I also note that in the last 300 million years or so, the earth has been overflowing with terrestrial plants and animals, despite the fact that there have been periods of much higher temperatures.
Looking deeply into the paper, the message I see is "I can apply fractional calculus to climate science". I don't know what fractional calculus is, but the message of that paper is that he can do it, and apply it to fitting some climate data. That's not useless, but I'm not going to take an end of the world prediction seriously unless he justifies the content of the model.
And I expect something similar is going to happen as we go on, because it has happened before. The papers that are widely cited and seem to be taken seriously will be ones that predict some global warming, some sea level rise, and some modification of crop yields.
The others will be fringe journals where people make shrill predictions of impending starvation or extinction. Those will be cited in popular press magazines.
P.S. I don't want to give the impression I just waved this away. I can't say I followed the math, but I did follow a citation trail. It's not that this is a really owful paper, or even that it has nothing to say. However, its prediciton of oxygen starvation is not something I'll take too seriously unless I see it echoed by other reputable voices.