Related papers: Lyapunov inequality for a boundary value problem i…
We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.
We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated…
We derive a new Lyapunov type inequality for a boundary value problem involving both left Riemann--Liouville and right Caputo fractional derivatives in presence of natural conditions. Application to the corresponding eigenvalue problem is…
This paper establishes a Lyapunov-type inequality for a class of fractional boundary value problems (BVPs) involving two Hadamard fractional derivatives of different orders with Dirichlet boundary conditions. The method is based on the…
In this paper, we obtain Lyapunov type inequality for discrete fractional boundary value problem.
This paper investigates the existence of positive solutions for regular discrete second-order single-variable boundary value problems with mixed boundary conditions, including a nonhomogeneous Dirichlet boundary condition, of the form:…
In this work, we obtain a Lyapunov-type and a Hartman-Wintner-type inequalities for a linear and a nonlinear fractional differential equation with generalized Hilfer operator subject to Dirichlet-type boundary conditions. We prove existence…
In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…
In this article we establish a few Lyapunov-type inequalities for two-point discrete fractional boundary value problems involving Riemann-Liouville type backward differences. To illustrate the applicability of established results, we obtain…
In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our…
In this paper, we discuss the existence and uniqueness of solutions of a boundary value problem for a fractional differential equation of order $\alpha\in(2,3)$, involving a general form of fractional derivative. First, we prove an…
A survey of results on Lyapunov-type inequalities for fractional differential equations associated with a variety of boundary conditions is presented. This includes Dirichlet, mixed, Robin, fractional, Sturm-Liouville, integral, nonlocal,…
In this paper we study the existence of solutions for nonlinear boundary value problems ({\phi}(u' ))' = f(t,u,u'), l(u,u')=0 where l(u,u') =0 denotes the Dirichlet or mixed conditions on [0, T], {\phi} is a bounded, singular or classic…
In this paper, we focus on the existence and uniqueness of solutions of boundary value problems for a coupled system of fractional differential equations with four-point boundary conditions involving $\psi$-Caputo fractional derivatives.…
In this paper Lyapunov type inequality is developed for hybrid fractional boundary value problem involving the prabhakar fractional derivative.
In this paper, we consider a linear fractional differential equation with fractional boundary conditions. First, by obtaining Green's function, we derive the Lyapunov-type inequalities for such boundary value problems. Furthermore, we use…
In this paper, we prove the existence of a weak solution for the Dirichlet boundary value problem related to the $p(x)-$Laplacian $$ -\mbox{div}(|\nabla u|^{p(x)-2}\nabla u)+u\in -[\underline{g}(x,u),\overline{g}(x,u)], $$ by using the…
In this paper, Lyapunov type inequality is establish for fractional boundary value problem involving the k-Prabhakar fractional derivative.
Here we study the Dirichlet problem for first order linear and quasi-linear hyperbolic PDEs on a simply connected bounded domain of $\R^2$, where the domain has an interior outflow set and a mere inflow boundary. By means of a Lyapunov…
The aim of this paper is to obtain the existence of solution for the fractional p-Laplacian Dirichlet problem with mixed derivatives \begin{eqnarray*} &{_{t}}D_{T}^{\alpha}\left(|_{0}D_{t}^{\alpha}u(t))|^{p-2}{_{0}}D_{t}^{\alpha}u(t)\right)…