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Nyamoradi, N., Alaei Dizaji, H.. (1393). Existence solutions for nonlocal fractional differential equation with nonlinear boundary conditions. , 38(4), 455-461. doi: 10.22099/ijsts.2014.2562
N. Nyamoradi; H. Alaei Dizaji. "Existence solutions for nonlocal fractional differential equation with nonlinear boundary conditions". , 38, 4, 1393, 455-461. doi: 10.22099/ijsts.2014.2562
Nyamoradi, N., Alaei Dizaji, H.. (1393). 'Existence solutions for nonlocal fractional differential equation with nonlinear boundary conditions', , 38(4), pp. 455-461. doi: 10.22099/ijsts.2014.2562
Nyamoradi, N., Alaei Dizaji, H.. Existence solutions for nonlocal fractional differential equation with nonlinear boundary conditions. , 1393; 38(4): 455-461. doi: 10.22099/ijsts.2014.2562

Existence solutions for nonlocal fractional differential equation with nonlinear boundary conditions

Iranian Journal of Science
مقاله 8، دوره 38، شماره 4، اسفند 2014، صفحه 455-461    اصل مقاله (435.64 K)
نوع مقاله: Regular Paper
شناسه دیجیتال (DOI): 10.22099/ijsts.2014.2562
نویسندگان
N. Nyamoradi* 1؛ H. Alaei Dizaji2
1Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran
2Department of Mathematics, Payame Noor University, Iran
چکیده
 
In this paper, by employing the Guo-Krasnoselskii fixed point theorem in a cone, we study the existence of positive solutions to the following nonlocal fractional boundary value problems
{ 𝐷0+ 𝛼 𝑢(𝑡) = 𝑓(𝑡, 𝑢(𝑡)), 𝑡 ∈ (0,1), 𝑢𝑡 + 𝑢′(0) = 12 [𝐻1(𝜑𝑢) + ∫ 𝐻2 𝐸(𝑠 𝑢𝑠)𝑑𝑠 , 𝑢1) + 𝑢′(1) = 0, c
where c𝐷0+ 𝛼is the standard Caputo derivative of order 𝛼 1 < 𝛼< 2, 𝐸⊆ (0,1) is some measurable set. We provide conditions on 𝑓 𝐻1, 𝐻2 and 𝜑such that the problem exhibits at least one positive solution.
کلیدواژه‌ها
Cone؛ fixed point theorem؛ standard Caputo؛ Derivative
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