scholarly journals A Lyapunov-type inequality for a fractional differential equation under Sturm-Liouville boundary conditions

2017 ◽  
pp. 139-148 ◽  
Author(s):  
Yo yu Wang ◽  
Shuil an Liang ◽  
Chen ue Xia
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Type Inequality ◽  
Sturm Liouville ◽  
Fractional Differential ◽  
Lyapunov Type Inequality

A Lyapunov-type inequality for a fractional boundary value problem

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Rui Ferreira
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Type Inequality ◽  
Fractional Boundary Value Problem ◽  
Real Zeros ◽  
Fractional Differential ◽  
Type Boundary ◽  
Lyapunov Type Inequality

AbstractIn this work we obtain a Lyapunov-type inequality for a fractional differential equation subject to Dirichlet-type boundary conditions. Moreover, we apply this inequality to deduce a criteria for the nonexistence of real zeros of a certain Mittag-Leffler function.

scholarly journals Existence and uniqueness of mild solutions for a fractional differential equation under Sturm-Liouville boundary conditions when the data function is of Lipschitzian type

2020 ◽  
Vol 53 (1) ◽  
pp. 167-173
Author(s):  
Jackie Harjani ◽  
Belen López ◽  
Kishin Sadarangani
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Type Inequality ◽  
Sufficient Condition ◽  
Fractional Boundary Value Problem ◽  
Data Function ◽  
Sturm Liouville ◽  
Fractional Differential ◽  
Lyapunov Type Inequality

AbstractIn this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of Lipschitzian type. Moreover, we present an application of our result to the eigenvalues problem and its connection with a Lyapunov-type inequality.

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