Results 1 to 10 of about 29,963 (198)
A Lyapunov type inequality for fractional operators with nonsingular Mittag-Leffler kernel [PDF]
Journal of Inequalities and Applications, 2017 In this article, we extend fractional operators with nonsingular Mittag-Leffler kernels, a study initiated recently by Atangana and Baleanu, from order α ∈ [ 0 , 1 ] $\alpha\in[0,1]$ to higher arbitrary order and we formulate their correspondent integral
Thabet Abdeljawad
doaj +2 more sources
Investigation of a Lyapunov delta-type inequality with respect to a discrete fractional Green’s function [PDF]
Scientific ReportsThis article considers a Lyapunov delta-type inequality with Green’s functions including fractional falling functions. We define a fractional difference problem of Riemann-Liouville type with a fractional boundary condition and, using the Green’s ...
Pshtiwan Othman Mohammed, Meraa Arab
doaj +2 more sources
A Lyapunov-Type Inequality for Partial Differential Equation Involving the Mixed Caputo Derivative
Mathematics, 2020 In this work, we derive a Lyapunov-type inequality for a partial differential equation on a rectangular domain with the mixed Caputo derivative subject to Dirichlet-type boundary conditions.
Jie Wang, Shuqin Zhang
doaj +3 more sources
Sharp Lyapunov inequalities and the emergence of chaos in discrete fractional systems [PDF]
Scientific ReportsIn this article, novel results on the maximality of discrete fractional Green’s functions are established and corresponding explicit Lyapunov inequalities for delta fractional systems, with applications to chaos analysis and robust control design, are ...
Meraa Arab +3 more
doaj +2 more sources
Lyapunov-type inequality and solution for a fractional differential equation
Journal of Inequalities and Applications, 2020 In this paper, we consider the linear fractional differential equation By obtaining the Green’s function we derive the Lyapunov-type inequality for such a boundary value problem.
Dexiang Ma, Zifa Yang
doaj +1 more source
Asymptotic controllability and optimal control [PDF]
, 2012 We consider a control problem where the state must reach asymptotically a target while paying an integral payoff with a non-negative Lagrangian. The dynamics is just continuous, and no assumptions are made on the zero level set of the Lagrangian. Through
Motta, Monica, Rampazzo, Franco
core +3 more sources
Journal of Inequalities and Applications, 2019 A Lyapunov-type inequality is derived for a nonlinear fractional boundary value problem involving Caputo-type fractional derivative. The obtained inequality provides a necessary condition for the existence of nontrivial solutions to the considered ...
Mohamed Jleli, Bessem Samet, Yong Zhou
doaj +1 more source
A generalized Lyapunov inequality for a higher-order fractional boundary value problem
Journal of Inequalities and Applications, 2016 In the paper, we establish a Lyapunov inequality and two Lyapunov-type inequalities for a higher-order fractional boundary value problem with a controllable nonlinear term. Two applications are discussed.
Dexiang Ma
doaj +1 more source
Bernstein type's concentration inequalities for symmetric Markov processes [PDF]
, 2010 Using the method of transportation-information inequality introduced in \cite{GLWY}, we establish Bernstein type's concentration inequalities for empirical means $\frac 1t \int_0^t g(X_s)ds$ where $g$ is a unbounded observable of the symmetric Markov ...
Gao, Fuqing, Guillin, Arnaud, Wu, Liming
core +5 more sources
Journal of Inequalities and Applications, 2019 This paper is devoted to studying the Lyapunov-type inequality for sequential Hilfer fractional boundary value problems. We first provide some properties of Hilfer fractional derivative, and then establish Lyapunov-type inequalities for a sequential ...
Wei Zhang, Wenbin Liu
doaj +1 more source