University of TabrizComputational Methods for Differential Equations2345-39825220170401Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations1581696077ENKamalShahDepartment of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, PakistanSalmanZebDepartment of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, PakistanRahmat AliKhanDepartment of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, PakistanJournal Article20170114This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type<br />−Dq<br />0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,<br />u(0) = 0, u(1) =<br />m−2<br />∑ i<br />=1<br />δiu(ηi),<br />where Dq<br />0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) with<br />m−2<br />∑<br />i=1<br />δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ∞) is a continuous function. We use some classical results of fixed point theory to obtain sufficient conditions for the existence and multiplicity results of positive solutions to the problem under consideration. In order to show the applicability of our results, we provide some examples.https://cmde.tabrizu.ac.ir/article_6077_786926df406ec4f5042d803915a6e8dd.pdf