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.
Zeb, Salman and Ali Khan, Rahmat
"Sufficient Conditions for Existence and Uniqueness of Solutions to Fractional Order Multi-Point Boundary Value Problems,"
Progress in Fractional Differentiation & Applications: Vol. 1
, Article 7.
Available at: https://dc.naturalspublishing.com/pfda/vol1/iss4/7