scholarly journals A Lyapunov-Type Inequality for a Fractional Differential Equation under a Robin Boundary Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Mohamed Jleli ◽  
Lakhdar Ragoub ◽  
Bessem Samet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fractional Differential Equations ◽  
Type Inequality ◽  
Robin Boundary Condition ◽  
Robin Boundary Conditions ◽  
Real Zeros ◽  
Fractional Differential ◽  
Robin Boundary ◽  
Lyapunov Type Inequality

We establish a new Lyapunov-type inequality for a class of fractional differential equations under Robin boundary conditions. The obtained inequality is used to obtain an interval where a linear combination of certain Mittag-Leffler functions has no real zeros.

scholarly journals Numerical Solution of Heat Equation with Singular Robin Boundary Condition

2018 ◽  
Vol 19 (2) ◽  
pp. 209
Author(s):  
German Lozada-Cruz ◽  
Cosme Eustaquio Rubio-Mercedes ◽  
Junior Rodrigues-Ribeiro
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Numerical Solution ◽  
Dirichlet Boundary ◽  
Robin Boundary Condition ◽  
Robin Boundary Conditions ◽  
Positive Parameter ◽  
One Dimensional ◽  
Small Positive Parameter ◽  
Robin Boundary

In this work we study the numerical solution of one-dimensional heatdiffusion equation with a small positive parameter subject to Robin boundary conditions. The simulations examples lead us to conclude that the numerical solutionsof the differential equation with Robin boundary condition are very close of theanalytic solution of the problem with homogeneous Dirichlet boundary conditionswhen tends to zero

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 The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xia Wang ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Type Inequality ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Maximum Value ◽  
Fractional Differential ◽  
Lyapunov Type Inequality

In this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding equations. As for application, we study the eigenvalue problem in the sense of CFR.

Multiple solutions for an elliptic system with indefinite Robin boundary conditions

2017 ◽  
Vol 8 (1) ◽  
pp. 603-614 ◽  
Author(s):  
Pablo Amster
Keyword(s):  
Boundary Condition ◽  
Elliptic System ◽  
Multiple Solutions ◽  
Robin Boundary Condition ◽  
Robin Boundary Conditions ◽  
Precise Calculation ◽  
Scalar Operator ◽  
Point Operator ◽  
Robin Boundary ◽  
Linear Scalar

Abstract Multiplicity of solutions is proved for an elliptic system with an indefinite Robin boundary condition under an assumption that links the linearisation at 0 and the eigenvalues of the associated linear scalar operator. Our result is based on a precise calculation of the topological degree of a suitable fixed point operator over large and small balls.

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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