scholarly journals Lyapunov-type inequality for a fractional differential equation with fractional boundary conditions

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Ji Rong ◽  
Chuanzhi Bai
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Type Inequality ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
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 Hartman-Type and Lyapunov-Type Inequalities for a Fractional Differential Equation with Fractional Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Imed Bachar ◽  
Hassan Eltayeb
Keyword(s):  
Differential Equation ◽  
Lower Bound ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

We prove Hartman-type and Lyapunov-type inequalities for a class of Riemann–Liouville fractional boundary value problems with fractional boundary conditions. Some applications including a lower bound for the corresponding eigenvalue problem are obtained.

scholarly journals Analysis of some Katugampola fractional differential equations with fractional boundary conditions

2021 ◽  
Vol 18 (6) ◽  
pp. 7269-7279
Author(s):  
Barbara Łupińska ◽  
◽  
Ewa Schmeidel
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Fractional Differential Equations ◽  
Type Inequality ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
Lyapunov Type Inequality

<abstract><p>In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results.</p></abstract>

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