Results 11 to 20 of about 25,247 (223)

Fractional operators with exponential kernels and a Lyapunov type inequality

Advances in Difference Equations, 2017
In this article, we extend fractional calculus with nonsingular exponential kernels, initiated recently by Caputo and Fabrizio, to higher order. The extension is given to both left and right fractional derivatives and integrals.
Thabet Abdeljawad
doaj   +2 more sources

A Lyapunov-Type Inequality for a Fractional Differential Equation under a Robin Boundary Condition [PDF]

Journal of Function Spaces, 2015
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
Mohamed Jleli, Lakhdar Ragoub, Bessem Samet   +2 more
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   +2 more sources

A Lyapunov type inequality for indefinite weights and eigenvalue homogenization [PDF]

Proceedings of the American Mathematical Society, 2015
12 ...
Salort, Ariel Martin, Fernandez Bonder, Julian, Pinasco, Juan Pablo   +2 more
openaire   +5 more sources

A Lyapunov-Type Inequality for a Laplacian System on a Rectangular Domain with Zero Dirichlet Boundary Conditions

Mathematics, 2019
We consider a coupled system of partial differential equations involving Laplacian operator, on a rectangular domain with zero Dirichlet boundary conditions. A Lyapunov-type inequality related to this problem is derived.
Mohamed Jleli, Bessem Samet
doaj   +2 more sources

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

Journal of Function Spaces, 2018
In this paper, we research CFR fractional differential equations with the derivative of order ...
Xia Wang, Run Xu
doaj   +2 more sources

Lyapunov-type inequalities for nonlinear fractional differential equations and systems involving Caputo-type fractional derivatives

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

Dynamic multi‐objective optimisation of complex networks based on evolutionary computation

IET Networks, EarlyView., 2022
Abstract As the problems concerning the number of information to be optimised is increasing, the optimisation level is getting higher, the target information is more diversified, and the algorithms are becoming more complex; the traditional algorithms such as particle swarm and differential evolution are far from being able to deal with this situation ...
Linfeng Huang
wiley   +1 more source

Lyapunov-type inequalities for sequential fractional boundary value problems using Hilfer’s fractional derivative

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