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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
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Generalizations of "standard" calculus
This could be an answer for your last question: if you define $\frac{\Delta_t}{t}$ as $\frac{f(x+t)-f(x)}{t}$ for $t>0$ and you solve $\frac{\Delta_t}{t}(f)=f$ you obtain the solution $$f(x)=\left((1+ …