Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter

2014 ◽  
Vol 19 (8) ◽  
pp. 2820-2827 ◽  
Author(s):  
Chengbo Zhai ◽  
Li Xu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Point Boundary ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

scholarly journals Triple positive solutions for semipositone fractional differential equations m-point boundary value problems with singularities and p–q-order derivatives

2018 ◽  
Vol 23 (6) ◽  
pp. 889-903 ◽  
Author(s):  
Xingqiu Zhang ◽  
Zhuyan Shao ◽  
Qiuyan Zhong ◽  
Zengqin Zhao
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
Height Functions ◽  
Triple Positive Solutions ◽  
Fractional Differential ◽  
Bounded Sets

In this paper, by means of Leggett–Williams and Guo–Krasnosel'skii fixed point theorems, together with height functions of the nonlinearity on different bounded sets, triple positive solutions are obtained for some fractional differential equations with p–q-order derivatives involved in multi-point boundary value conditions. The nonlinearity may not only take negative infinity but also may permit singularities on both the time and the space variables.

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