scholarly journals The Uniqueness of Solution for a Class of Fractional Order Nonlinear Systems withp-Laplacian Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jun-qi He ◽  
Xue-li Song
Keyword(s):  
Nonlinear Systems ◽  
Boundary Conditions ◽  
Fractional Order ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Uniqueness Of Solution ◽  
Laplacian Operator ◽  
Uniqueness Of Solutions ◽  
Criterion Of Uniqueness

We are concerned with the uniqueness of solutions for a class ofp-Laplacian fractional order nonlinear systems with nonlocal boundary conditions. Based on some properties of thep-Laplacian operator, the criterion of uniqueness for solutions is established.

Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions

2015 ◽  
Vol 65 (6) ◽  
Author(s):  
Zhenhai Liu ◽  
Jingyun Lv
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Contraction Mapping ◽  
Nonlocal Boundary ◽  
Impulsive Differential Equations ◽  
Nonlocal Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

AbstractIn this paper, we prove the existence and uniqueness of solutions of fractional impulsive differential equations with nonlocal boundary conditions by applying the contraction mapping principle.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Jiang ◽  
Zhong Chen ◽  
Ning Hu ◽  
Yali Chen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Reproducing Kernel ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Orthonormal Bases ◽  
Fractional Differential

AbstractIn recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal bases of a reproducing kernel space. The nonlocal boundary conditions are transformed into operator equations, which are involved in finding the collocation coefficients as constrain conditions. In theory, the convergent order and stability analysis of the proposed method are presented rigorously. Finally, numerical examples show the stability, accuracy and effectiveness of the method.

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