TY - JOUR
ID - 6077
TI - Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Shah, Kamal
AU - Zeb, Salman
AU - Khan, Rahmat Ali
AD - Department of Mathematics, University of Malakand,
Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Y1 - 2017
PY - 2017
VL - 5
IS - 2
SP - 158
EP - 169
KW - Fractional differential equations
KW - Boundary value problems
KW - Positive solutions
KW - Green’s function
KW - fixed point theorem
DO -
N2 - This 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−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi 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.
UR - https://cmde.tabrizu.ac.ir/article_6077.html
L1 - https://cmde.tabrizu.ac.ir/article_6077_786926df406ec4f5042d803915a6e8dd.pdf
ER -