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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