# Tagged Questions

Questions on the differentiation/integration of functions to arbitrary order. Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers or complex number powers of the differentiation and integration operators.

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### Simplify into partial fractions $\frac{x^8}{x(x^2+1)^2}$

Simplify into partial fractions $$\frac{x^8}{x(x^2+1)^2}$$ I tried many times but after a point a $"x"$ of denominator vanishes. Can't all fraction be shown in its partial fraction? If not ...
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### Continuity of Fractional Derivative

Here's a continuity result that I believe to be true, but I don't know if my assumptions are minimal (i.e. does it still go through with just assuming continuity or something slightly weaker ...
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### Difference between terminal value problem and initial value problem of ODE r FDE?

What is difference between terminal value problem and initial value problem of differential equations. Kindly give an example.
Main Question What is the expansion of $d^{1+\epsilon}?$ Background I noticed the following trick (sometimes more laborious) to directly differentiate $f(x)$ twice without differentiating it even ...