2017
DOI: 10.1186/s13662-017-1157-7
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Existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations

Abstract: In the article, the existence and uniqueness of positive solutions for a class of fractional differential equation with nonlinear boundary conditions are discussed. By applying some fixed point theorems on cone, we gain a unique positive solution and construct two iterative sequences to approximate the solution. Moreover, as applications of our main results, some examples are also presented.

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Cited by 17 publications
(24 citation statements)
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“…The two-side restriction conditions (2.1) and (2.19)-(2.21) with respect to the ordering relations of nonlinear operators in Theorems 2.1 and 2.4 are a kind of more general conditions than those in [6,10,11,13,16], from which we can not only deduce the existence but also the uniqueness of fixed points. …”
Section: Resultsmentioning
confidence: 92%
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“…The two-side restriction conditions (2.1) and (2.19)-(2.21) with respect to the ordering relations of nonlinear operators in Theorems 2.1 and 2.4 are a kind of more general conditions than those in [6,10,11,13,16], from which we can not only deduce the existence but also the uniqueness of fixed points. …”
Section: Resultsmentioning
confidence: 92%
“…Because the conditions in Theorems 2.1 and 2.4 of this paper are more general, their applications to nonlinear differential and integral equations must be extensive under the two side ordering relations conditions. Moreover, this also means that our results can not be obtained by the proof methods and results in [6,10,11,13,16].…”
Section: An Applicationmentioning
confidence: 84%
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“…More recently, in connection with broad research on the mathematical modeling of systems, the description of hereditary properties of various materials and the optimal control theory, it has become necessary to investigate boundary value problems of fractional differential equations as the nonlocal characteristics of the corresponding fractional-order operators [5,6,[8][9][10]18,20,[24][25][26][27]29,31,32]. Moreover, these equations are always completely controllable, meanwhile the research on fractional q-differential equation boundary value problems is in a stage of rapid development; one can see [2,3,7,14,18,23,29,30,33] and the references cited therein.…”
Section: Introductionmentioning
confidence: 99%