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Author Country (or Countries)

Pakistan

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.

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