The tag has no wiki summary.

learn more… | top users | synonyms

2
votes
0answers
76 views

A question about fractional integrals

I am starting from Theorem 3.4 in Struwe's book Variational methods. The authors proves an existence result for a problem with critical growth. I would like to replace the laplacian with the ...
1
vote
0answers
92 views

A fractional calculus eigenvalue problem

One set of eigenfunction for the following fractional integral operator is $f(z)=e^{-bz}$ for any constant Re$b>0$, with eigenvalue $\lambda=\frac{\Gamma(\alpha)}{b^\alpha}$, $$\int_z^\infty ...
0
votes
0answers
21 views

Diffusion maps for non-Markov

Diffusion maps based on the work of Coifman and Lafon use concepts from Markov chains and heat diffusions. Have there been work to extend diffusion maps to non-Markovian or fractional heat ...
0
votes
0answers
79 views

Natural integration constant for normal and discrete integration: is there a connection?

It is often assumed that integration, unlike differentiation is defined only to an arbitrary constant. So the antiderivative function is often left undefined or postulated to be zero in zero. But I ...
0
votes
0answers
123 views

Fractional Derivative of A specific function

I've tried and tried to do this problem myself, but I've hit some snags on the way. I'm trying to take the fractional derivative of: $f(x)=1+n^{-x}$ where n is an integer and $n\geq2$ and $x>1$. ...
0
votes
0answers
129 views

Fractional Derivatives Of Sums

I have a question regarding the definition of a fractional derivative. I've searched, but I can't find a definition of fractional derivatives that explain the concept in terms of an operator on some ...
0
votes
0answers
60 views

Fractional/complex powers of integrals

I'm wondering if there is a way to represent a fractional power of an integral as a function of the integrand in the following sense: The binomial theorem for complex/fractional exponents represents a ...
0
votes
0answers
256 views

Chain rule for fractional derivative defined via Fourier transform

It is well known that in the case of integer order differentiation the formula $\partial_{x}f(x,u(x))=\partial_{u}f\cdot \partial_{x}u+\partial_{x}f\cdot u$ holds. If we define fractional derivative ...
0
votes
0answers
266 views

Relation between interpolation spaces and besov spaces

Consider the following two norms: The interpolation norm: 1) $\|u; [L_2,\dot H_1^{\infty}]_{1/3,\infty}\| := \sup_{s > 0} \inf_{u=u_0+u_1} \frac{\|u_0\|_{L^2}}{s^{1/2}} + s \|\partial_x ...