Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations

	Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations
Computational Methods for Differential Equations
مقاله 5، دوره 5، شماره 2، تیر 2017، صفحه 158-169 اصل مقاله (163.41 K)
نوع مقاله: Research Paper
نویسندگان
Kamal Shah^* ؛ Salman Zeb؛ Rahmat Ali Khan
Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
چکیده
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.
کلیدواژه‌ها
Fractional differential equations؛ Boundary value problems؛ Positive solutions؛ Green’s function؛ fixed point theorem

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