Related papers: Sharp estimates for the unique solution of the Had…
We prove several integral Harnack-type inequalities for local weak solutions of parabolic equations with measurable and bounded coefficients, describing singular s-fractional p-Laplacian diffusion. Then we apply the aforementioned estimates…
This paper deals with the existence and uniqueness of solutions for a nonlinear boundary value problem involving a sequential $\psi$-Hilfer fractional integro-differential equations with nonlocal boundary conditions. The existence and…
An estimate of Green's function of the bounded solutions problem for the ordinary differential equation $x'(t)-Bx(t)=f(t)$ is proposed. It is assumed that the matrix coefficient $B$ is triangular. This estimate is a generalization of the…
The aim of the present paper is to study the existence, uniqueness and some other properties of solutions of a certain partial dynamic integrodifferential equations. The Banach fixed point theorem and certain fundamental inequality with…
We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in particular, the sign of the normal derivative of such…
In this paper, we analyze a second-order differential equation with a piecewise constant argument and reflection coupled to periodic boundary conditions. Our main contribution is the construction of the related Green's function and a…
In this paper, we propose a numerical method for computing Hadamard finite-part integrals with an integral-power singularity at an endpoint, the part of the divergent integral which is finite as a limiting procedure. In the proposed method,…
In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the…
We study how the solution of the two-dimensional Dirichlet boundary problem for smooth simply connected domains depends upon variations of the data of the problem. We show that the Hadamard formula for the variation of the Dirichlet Green…
This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of…
We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order $\alpha\in (3/2,2)$ on the unit interval $(0,1)$. The standard Galerkin finite element approximation converges slowly due to the presence of…
In this paper, we study existence results for initial value problems for hybrid fractional integro-differential equations. Our investigation is based on the Dhage hybrid fixed point theorem. Some fundamental fractional differential…
We obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of a smooth function. When considering finite sums only, an upper bound for the error is given. Numerical simulations show the efficiency of…
In this paper we present an inexact proximal point method for variational inequality problem on Hadamard manifolds and study its convergence properties. The proposed algorithm is inexact in two sense. First, each proximal subproblem is…
In this paper, we investigate the unique solvability of a mixed boundary value problem for a fractional partial differential equation featuring a degenerate coefficient. By introducing a novel operator and applying the method of separation…
A sharp double-sided Harnack bound is derived for positive solutions of a fractional order heat equation.
The inhomogenous time-fractional telegraph equation with Caputo derevatives with constant coefficients is considered. For considered equation the general representation of regular solution in rectangular domain is obtained, and the…
In Boundary Element Method, Green's function with no boundary conditions is used for solving Laplace's equation with Dirichlet boundary condition. To determine the gradient of solution on the boundary, we need to solve the boundary integral…
We find the nodes that minimise divided differences and use them to find the sharp constant in a sublevel set estimate. We also find the sharp constant in the first instance of the van der Corput Lemma using a complex mean value theorem for…
This paper deals with an extremal problem for harmonic functions in the unit ball of $\mathbf{R}^n$. We are concerned with the pointwise sharp estimates for the gradient of real--valued bounded harmonic functions. Our main result may be…