2013
DOI: 10.2478/s11534-013-0238-9
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Existence of positive solutions for nonlocal boundary value problem of fractional differential equation

Abstract: Abstract:In this paper, we study a type of nonlinear fractional differential equations multi-point boundary value problem with fractional derivative in the boundary conditions. By using the upper and lower solutions method and fixed point theorems, some results for the existence of positive solutions for the boundary value problem are established. Some examples are also given to illustrate our results.PACS (2008)

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Cited by 3 publications
(3 citation statements)
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“…Many important results for certain boundary value conditions related to the fractional differential equations had been obtained, for example, twopoint boundary value problem, multi-point boundary value problem, integral boundary value problem and so on, see [6][7][8][9][10][11][12][13][14][15][16].…”
Section: Introductionmentioning
confidence: 99%
“…Many important results for certain boundary value conditions related to the fractional differential equations had been obtained, for example, twopoint boundary value problem, multi-point boundary value problem, integral boundary value problem and so on, see [6][7][8][9][10][11][12][13][14][15][16].…”
Section: Introductionmentioning
confidence: 99%
“…In recent years, the theory of fractional order differential equations is developing to an important area of investigation, which is widely used in multiple fields like non‐Newtonian mechanics, nonlinear elasticity and glaciology, combustion theory, population biology, and complex geometry and patterns; for details and examples, see and the references therein. We notice that lots of systems with short‐term perturbations are often described by using impulsive differential equations.…”
Section: Introductionmentioning
confidence: 99%
“…With the development of mathematics, fractional derivative occurs more and more frequently in different research areas, such as physics, mechanics, electricity, and economics (see [1,2]). At the same time, significant progress has also been made on the studies of fractional differential equations (see [3][4][5][6][7][8][9][10][11][12]).…”
Section: Introductionmentioning
confidence: 99%