Existence and uniqueness of nontrivial solutions for eigenvalue boundary value problem of nonlinear fractional differential equation

2013 ◽  
Vol 60 (2) ◽  
pp. 429-445 ◽  
Author(s):  
Xiaosong Tang
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Nontrivial Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

scholarly journals Existence and Uniqueness of Solutions for BVP of Nonlinear Fractional Differential Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Cheng-Min Su ◽  
Jian-Ping Sun ◽  
Ya-Hong Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Fractional Differential

In this paper, we study the existence and uniqueness of solutions for the following boundary value problem of nonlinear fractional differential equation: D0+qCut=ft,ut,  t∈0,1, u0=u′′0=0,  D0+σ1Cu1=λI0+σ2u1, where 2<q<3, 0<σ1≤1, σ2>0, and λ≠Γ2+σ2/Γ2-σ1. The main tools used are nonlinear alternative of Leray-Schauder type and Banach contraction principle.

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