Related papers: A note on a Pohozaev identity for the fractional G…
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
In this paper we develop a theory of linear differential systems analogous to the classical one for ODEs, including the obtaining of fundamental matrices, the development of a variation of parameters formula and the expression of the…
An analog of the Gelfand--Shilov estimate of the matrix exponential is proved for Green's function of the problem of bounded solutions of the ordinary differential equation $x'(t)-Ax(t)=f(t)$.
In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of the Green's function and the fixed point theorem in a…
The aim of this paper is to investigate Green's function for parabolic and elliptic systems satisfying a possibly nonlocal Robin-type boundary condition. We construct Green's function for parabolic systems with time-dependent coefficients…
This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary…
We extend the upper estimates obtained by M. Carlehed and B.-Y. Chen about the ratio of the classical and pluricomplex Green functions to the case of $\mathcal C^2$-smooth locally $\mathbb C$-convexifiable domains of finite type. We also…
The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ${\psi}-$Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
We establish an integration by parts formula in bounded domains for the higher order fractional Laplacian $(-\Delta)^s$ with $s>1$. We also obtain the Pohozaev identity for this operator. Both identities involve local boundary terms, and…
We derive the bilateral estimates for the module of continuity of the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces.
Our main aim is to study Green function for the fractional Hardy operator $P:=(-\Delta)^s -\frac{\theta}{|x|^{2s}}$ in $\mathbb{R}^N$, where $0<\theta<\Lambda_{N,s}$ and $\Lambda_{N,s}$ is the best constant in the fractional Hardy…
Using the new conformable fractional derivative, which differs from the Riemann-Liouville and Caputo fractional derivatives, we reformulate the second-order conjugate boundary value problem in this new setting. Utilizing the corresponding…
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…
Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, but instead of the usual equation…
A construction of the heat kernel diagonal is considered as element of generalized Zeta function, that, being meromorfic function, its gradient at the origin defines determinant of a differential operator in a technique for regularizing…
This note gives a higher-dimensional generalization of the classical formula cap(K) = exp(-V(E)) expressing the logarithmic capacity in terms of the residue at infinity of its Green's function. The proof uses arithmetic intersection theory.
On this thesis we present the fuzzy sets, fuzzy numbers, the fractional derivative and also we discuss the solution of the first order of fuzzy hybrid equation.
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…
In this paper, we studied the sufficient conditions for the existence of positive solutions to the boundary value problems of Caputo fractional difference equations depending on parameters with non local boundary conditions. We construct…