Progress in Fractional Differentiation & Applications
Article Title
Abstract
In this article, the following fractional order multi-point boundary value problem −cDqu(t) = f (t,u(t)) ; t ∈ J = [0,1],1 < q ≤ 2, u(0) = g(u(x )) , cDpu(1)− m−2 ? i=1 diu(hi) = h(u(h)) , 0 < p ≤ 1, is considered, where x ,h,di,hi ∈ (0,1) g,h ∈ C(J,R) are given functions and m−2 ? i=1 dihi < 1; f : J ×R → R is a continuous function and cDq is the Caputo derivative of fractional order q. The notation cDpu(1) means the value of cDpu(t) at t = 1. We use topological degree theory approach to establish sufficient conditions for existence and uniqueness of solutions. We provide an example to show the usefulness of our results.
Suggested Reviewers
N/A
Recommended Citation
Zeb, Salman and Ali Khan, Rahmat
(2015)
"Sufficient Conditions for Existence and Uniqueness of Solutions to Fractional Order Multi-Point Boundary Value Problems,"
Progress in Fractional Differentiation & Applications: Vol. 1:
Iss.
4, Article 7.
Available at:
https://digitalcommons.aaru.edu.jo/pfda/vol1/iss4/7