Uniqueness of solutions for a fractional thermostat model

In this paper, we present a sufficient condition for the uniqueness of solutions to a nonlocal fractional boundaryvalue problem which can be considered as the fractional version to the thermostat model. As application of ourresult, we study the eigenvalues problem associated and, moreover, we get a Lyapunov-type inequality.

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

Journal of Function Spaces ◽

10.1155/2018/5875108 ◽

2018 ◽

Vol 2018 ◽

pp. 1-7 ◽

Cited By ~ 1

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.

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Impulsive Boundary Value Problems for Planar Hamiltonian Systems

Abstract and Applied Analysis ◽

10.1155/2013/892475 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6

Author(s):

Zeynep Kayar ◽

Ağacık Zafer

Keyword(s):

Boundary Value Problem ◽

Hamiltonian Systems ◽

Existence And Uniqueness ◽

Boundary Value ◽

Type Inequality ◽

Existence And Uniqueness Theorem ◽

Uniqueness Of Solutions ◽

Impulsive Boundary Value Problems ◽

Impulsive Boundary Value Problem ◽

Lyapunov Type Inequality

We give an existence and uniqueness theorem for solutions of inhomogeneous impulsive boundary value problem (BVP) for planar Hamiltonian systems. Green's function that is needed for representing the solutions is obtained and its properties are listed. The uniqueness of solutions is connected to a Lyapunov type inequality for the corresponding homogeneous BVP.

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

Demonstratio Mathematica ◽

10.1515/dema-2020-0014 ◽

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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Lyapunov-type inequality for nonlinear systems with Riemann-Liouville fractional derivatives

Novi Sad Journal of Mathematics ◽

10.30755/nsjom.07194 ◽

2019 ◽

Vol 49 (2) ◽

pp. 17-34 ◽

Cited By ~ 1

Author(s):

Alireza Ansari ◽

Shiva Eshaghi ◽

Reza Khoshsiar Ghaziani

Keyword(s):

Nonlinear Systems ◽

Fractional Derivatives ◽

Type Inequality ◽

Lyapunov Type Inequality

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Lyapunov-type inequality for a class of odd-order differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2010.04.008 ◽

2010 ◽

Vol 234 (10) ◽

pp. 2962-2968 ◽

Cited By ~ 17

Author(s):

Xiaojing Yang ◽

Yong-In Kim ◽

Kueiming Lo

Keyword(s):

Differential Equations ◽

Type Inequality ◽

Odd Order ◽

Lyapunov Type Inequality

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Weak Orlicz–Hardy martingale spaces

International Journal of Mathematics ◽

10.1142/s0129167x15500627 ◽

2015 ◽

Vol 26 (08) ◽

pp. 1550062 ◽

Cited By ~ 10

Author(s):

Yong Jiao ◽

Lian Wu ◽

Lihua Peng

Keyword(s):

Atomic Decomposition ◽

Type Inequality ◽

Sublinear Operator ◽

Sufficient Condition ◽

Concave Functions ◽

Atomic Decompositions ◽

Stochastic Basis ◽

Decomposition Theorems

In this paper, several weak Orlicz–Hardy martingale spaces associated with concave functions are introduced, and some weak atomic decomposition theorems for them are established. With the help of weak atomic decompositions, a sufficient condition for a sublinear operator defined on the weak Orlicz–Hardy martingale spaces to be bounded is given. Further, we investigate the duality of weak Orlicz–Hardy martingale spaces and obtain a new John–Nirenberg type inequality when the stochastic basis is regular. These results can be regarded as weak versions of the Orlicz–Hardy martingale spaces due to Miyamoto, Nakai and Sadasue.

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