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Sufficient Conditions for Existence and Uniqueness of Solutions to Fractional Order Multi-Point Boundary Value Problems |
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PP: 303-311 |
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doi:10.18576/pfda/010407
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Author(s) |
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Salman Zeb,
Rahmat Ali Khan,
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Abstract |
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| 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
å
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
å
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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