Fractional differential equations: alpha-entire solutions, regular and irregular singularities

Details Fractional differential equations: alpha-entire solutions, regular and irregular singularities Fractional differential equations: alpha-entire solutions, regular and irregular singularities

2008-06-11

arxiv.org/abs/0806.1826v2

Mathematics

Classical Analysis and ODEs

20 pages; to appear in Fractional Calculus and Applied Analysis

Scientific paper

We consider fractional differential equations of order $\alpha \in (0,1)$ for functions of one independent variable $t\in (0,\infty)$ with the Riemann-Liouville and Caputo-Dzhrbashyan fractional derivatives. A precise estimate for the order of growth of $\alpha$-entire solutions is given. An analog of the Frobenius method for systems with regular singularity is developed. For a model example of an equation with a kind of an irregular singularity, a series for a formal solution is shown to be convergent for $t>0$ (if $\alpha$ is an irrational number poorly approximated by rational ones) but divergent in the distribution sense.

Affiliated with

Also associated with

No associations

Rating

Fractional differential equations: alpha-entire solutions, regular and irregular singularities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fractional differential equations: alpha-entire solutions, regular and irregular singularities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fractional differential equations: alpha-entire solutions, regular and irregular singularities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-264985