scholarly journals The unique positive solution for fractional integro-differential equations on infinite intervals

ScienceAsia ◽  
2018 ◽  
Vol 44 (2) ◽  
pp. 118 ◽  
Author(s):  
Chengbo Zhai ◽  
Lifang Wei
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Unique Positive Solution ◽  
Infinite Intervals

scholarly journals Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift

2020 ◽  
Vol 25 (6) ◽  
pp. 1059-1078
Author(s):  
Kęstutis Kubilius
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Euler Scheme ◽  
Hurst Index ◽  
Unique Positive Solution ◽  
Backward Euler Scheme ◽  
Asymptotically Normal ◽  
Backward Euler ◽  
Locally Lipschitz ◽  
Strongly Consistent

Strongly consistent and asymptotically normal estimates of the Hurst index H are obtained for stochastic differential equations (SDEs) that have a unique positive solution. A strongly convergent approximation of the considered SDE solution is constructed using the backward Euler scheme. Moreover, it is proved that the Hurst estimator preserves its properties, if we replace the solution with its approximation.

scholarly journals Uniqueness of Successive Positive Solution for Nonlocal Singular Higher-Order Fractional Differential Equations Involving Arbitrary Derivatives

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Qiuyan Zhong ◽  
Xingqiu Zhang ◽  
Xinyi Lu ◽  
Zhengqing Fu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Higher Order ◽  
Unique Positive Solution ◽  
Mixed Monotone Operator ◽  
Iterative Schemes ◽  
Fractional Differential

In this article, by means of fixed point theorem on mixed monotone operator, we establish the uniqueness of positive solution for some nonlocal singular higher-order fractional differential equations involving arbitrary derivatives. We also give iterative schemes for approximating this unique positive solution.

scholarly journals Dynamical Behavior of the Stochastic Delay Mutualism System

2014 ◽  
Vol 2014 ◽  
pp. 1-19
Author(s):  
Peiyan Xia ◽  
Daqing Jiang ◽  
Xiaoyue Li
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Positive Solution ◽  
Asymptotic Property ◽  
Dynamical Behavior ◽  
Asymptotic Properties ◽  
Unique Positive Solution ◽  
Stochastic Delay ◽  
Mutualism System

We discuss the dynamical behavior of the stochastic delay three-specie mutualism system. We develop the technique for stochastic differential equations to deal with the asymptotic property. Using it we obtain the existence of the unique positive solution, the asymptotic properties, and the nonpersistence. Finally, we give the numerical examinations to illustrate our results.

scholarly journals Existence of Uniqueness and Nonexistence Results of Positive Solution for Fractional Differential Equations Integral Boundary Value Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yongqing Wang
Keyword(s):  
Differential Equations ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Integral Conditions ◽  
Interesting Point ◽  
Integral Boundary ◽  
Type Integral ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
Conjugate Type

In this paper, we consider a class of fractional differential equations with conjugate type integral conditions. Both the existence of uniqueness and nonexistence of positive solution are obtained by means of the iterative technique. The interesting point lies in that the assumption on nonlinearity is closely associated with the spectral radius corresponding to the relevant linear operator.

scholarly journals The Unique Positive Solution for Singular Hadamard Fractional Boundary Value Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Jinxiu Mao ◽  
Zengqin Zhao ◽  
Chenguang Wang
Keyword(s):  
Exact Solution ◽  
Convergence Rate ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Approximation Error ◽  
Iterative Solution ◽  
Unique Positive Solution ◽  
Fractional Boundary Value Problems

In this paper, we investigate singular Hadamard fractional boundary value problems. The existence and uniqueness of the exact iterative solution are established only by using an iterative algorithm. The iterative sequences have been proved to converge uniformly to the exact solution, and estimation of the approximation error and the convergence rate have also been derived.

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