Related papers: Fractional Kirchhoff-type and method of sub-supers…
This paper has two main purposes. In the first part, combining the nondegeneracy of the ground state with the Lyapunov--Schmidt reduction method, we prove the existence of multi-peak positive solutions to the singularly perturbed problem…
In this paper, we propose a new method to obtain new permutation polynomials over $\mathbb{F}_{q^2}$. Using this method, we extend many known permutation polynomials, which take the form $\sum_i(x^q-x+\delta)^{s_i}+L(x)$, where $L(x)$ is a…
In this paper we consider the following class of fractional Kirchhoff equations with critical growth: \begin{equation*} \left\{ \begin{array}{ll}…
In this paper, using the theory developed in [8], we obtain some results of a totally new type about a class of non-local problems. Here is a sample: Let $\Omega\subset {\bf R}^n$ be a smooth bounded domain, with $n\geq 4$, let $a, b,…
We deal with the higher-order fractional Laplacians by two methods: the integral method and the system method. The former depends on the integral equation equivalent to the differential equation. The latter works directly on the…
Assuming the generalized Riemann hypothesis, we rediscover and sharpen some of the best known results regarding the distribution of low-lying zeros of Dirichlet $L$-functions. This builds upon earlier work of Omar, which relies on the…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of…
The purpose of this paper is twofold. Firstly, we provide explicit and compact formulas for computing both Caputo and (modified) Riemann-Liouville (RL) fractional pseudospectral differentiation matrices (F-PSDMs) of any order at general…
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an…
In the present paper we study the existence of solutions for some nonlocal problems involving Orlicz-Sobolev spaces. The approach is based on sub-supersolutions.
We study nonnegative solutions to the Fractional Porous Medium Equation on a suitable class of connected, noncompact Riemannian manifolds. We provide existence and smoothing estimates for solutions, in an appropriate weak (dual) sense, for…
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…
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 study on the partial differential equations (systems) in the graph setting is a hot topic in recent years because of their applications to image processing and data clustering. Our motivation is to develop some existence results for…
The main purpose of this paper is to consider new sandwich pairs and investigate the existence of solution for a new class of fractional differential equations with $p$-Laplacian via variational methods in $\psi$-fractional space…
In this paper we prove the existence and uniqueness of positive classical solution of the fractional Laplacian with singular nonlinearity in a smooth bounded domain with zero Drichlet boundary conditions. By the method of sub-supersolution,…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…