Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
Abstract
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 −Dq 0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1, u(0) = 0, u(1) = m−2 ∑ i =1 δiu(ηi), where Dq 0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) with m−2 ∑ i=1 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.
Shah, K., Zeb, S., Khan, R. (2017). Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations. Computational Methods for Differential Equations, 5(2), 158-169.
MLA
Kamal Shah; Salman Zeb; Rahmat Ali Khan. "Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations". Computational Methods for Differential Equations, 5, 2, 2017, 158-169.
HARVARD
Shah, K., Zeb, S., Khan, R. (2017). 'Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations', Computational Methods for Differential Equations, 5(2), pp. 158-169.
VANCOUVER
Shah, K., Zeb, S., Khan, R. Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations. Computational Methods for Differential Equations, 2017; 5(2): 158-169.
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