Positive solutions for boundary value problems of nonlinear fractional differential equation

By Sihua Liang, Jihui Zhang. 2009

378 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/c3ab038e14769df69d9b40f6ad64dc805a28c141

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In Applied Mathematics

1. Lishan Liu
2. Yonghong Wu
3. J. Henderson
4. Rodica Luca
5. Zhanbing Bai
6. Qilin Song
7. Botao Chen
8. Xiao-jing Dong

In Modeling and Simulation

1. Lishan Liu
2. Yonghong Wu
3. J. Henderson
4. Rodica Luca
5. Zhanbing Bai
6. Botao Chen
7. Qilin Song
8. Xiao-jing Dong

Citations in the corpus

• Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences (2012, background): “Recently, an increasing interest in studying the existence of solutions for boundary value problems of fractional order functional differential equations has been observed [1–10].”
• The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems (2016, background): “Because of the crucial role played by nonlinear equations in applied science as well as mathematics, nonlinear functional analysis has been an active area of research, and nonlinear operators with connection to nonlinear (fractional) differential and integral equations have been extensively studied ”
• Method of upper and lower solutions for fractional differential equations (2012, background): “Hence, some meaningful results on this kind of problems have been obtained, (see [5, 6, 7, 8, 9, 10, 11, 12, 13]).”
• Positive solutions for a system of nonlocal fractional boundary value problems (2013, background): “For some recent developments on the topic, see [1]-[7], [9], [11]-[12], [19], [22] and the references therein.”
• On the existence of blow up solutions for a class of fractional differential equations (2014, background): “We noted that there were many works in respect of the existence of solutions for this fractional differential equations IVP, which were shown in [1, 2, 3, 4, 6, 7, 10, 11, 12, 13, 14] and the references therein.”
• Existence for fractional Dirichlet boundary value problem under barrier strip conditions (2017, positive): “After that, the idea was developed to deal with various fractional boundary value problems such as fractional boundary value problem at resonance [5, 6, 9, 10], Caputo fractional derivative problem [41], impulsive problem [7, 31, 33], nonlocal problem [4], integral boundary value problem [27], varia”
• Existence of Solutions for a Class of Coupled Fractional Differential Systems with Nonlocal Boundary Conditions (2017, neutral): “Then the boundary value problem CDα 0+x (t) = ω (t) , t ∈ [0, 1] , Dβ 0 y (t) = u (t) , t ∈ [0, 1] , x (0) = h (x) , x (1) = aIθ1 0 x (η) , y (0) = φ (y) , y (1) = bIθ2 0 y (ξ) (10)”