Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1211.39002
Goodrich, Christopher S.
Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions.
(English)
[J] Comput. Math. Appl. 61, No. 2, 191-202 (2011). ISSN 0898-1221

Summary: We consider a discrete fractional boundary value problem of the form - $\Delta^{\nu} y(t)=f(t+\nu - 1,y(t+\nu - 1)), y(\nu - 2)=g(y), y(\nu +b)=0$, where $f:[\nu-1,\dots,\nu+b-1]_{\bbfN_{\nu-2}}$ is continuous, $g:\cal C([\nu-2,\nu+b]_{\bbfN_{\nu-2}},\bbfR)$ is a given functional, and $1<\nu \leq 2$. We give a representation for the solution to this problem. Finally, we prove the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem, the Brouwer theorem, and the Krasnosel'skii theorem.
MSC 2000:
*39A10 Difference equations
26A33 Fractional derivatives and integrals (real functions)
39A12 Discrete version of topics in analysis

Keywords: discrete fractional calculus; boundary value problem; nonlocal boundary conditions; positive solution; existence and uniqueness of solution

Highlights
Master Server