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In this paper, we prove that there exists a unique weak solution to the mixed boundary value problem for a general class of semilinear second order elliptic partial differential equations with singular coefficients. Our approach is…
This study is concern with the numerical solution of the initial boundary value problem (IBVP) for the semilinear scale-invariant wave equation with damping and mass and power non-linearity. Numerical results of the aforementioned IBVP is…
An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the…
In this paper we consider the numerical solution of fractional terminal value problems (FDE-TVPs). In particular, the proposed procedure uses a Newton-type iteration which is particularly efficient when coupled with a recently-introduced…
In this article, we study an initial-boundary-value problem of a coupled KdV-KdV system on the half line $ \mathbb{R}^+ $ with non-homogeneous boundary conditions: \begin{equation*} \left\{ \begin{array}{l} u_t+v_x+u u_x+v_{xxx}=0, \quad…
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation \begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+\lambda…
We study an initial value problem for the one-dimensional non-stationary linear Schr\"odinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems…
A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…
A boundary value problem associated to the difference equation with advanced argument \begin{equation} \label{*}\Delta\bigl (a_{n}\Phi(\Delta x_{n})\bigr)+b_{n}\Phi(x_{n+p} )=0,\ \ n\geq1 \tag{$*$} \end{equation} is presented, where…
We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Using the Krasnosel'skii fixed point theorem we prove, via the…
Singular boundary value problems (SBVPs) arise in various fields of Mathematics, Engineering and Physics such as boundary layer theory, gas dynamics, nuclear physics, nonlinear optics, etc. The present monograph is devoted to systems of…
In this paper, we solve explicitly and analyze rigorously inhomogeneous initial-boundary-value problems (IBVP) for several fourth-order variations of the traditional diffusion equation and the associated linearized Cahn-Hilliard (C-H) model…
In this article, we obtain existence and uniqueness results to some problems involving complex nonlinear fractional differential equations (FDEs) in the closed unit disc of C. By help of these results, we prove that some IVPs for some…
We consider the initial boundary value problem (IBVP) for a non-local scalar conservation laws in one space dimension. The non-local operator in the flux function is not a mere convolution product, but it is assumed to be aware of…
We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve…
This paper concerns the initial-boundary value problem (IBVP) of the Kawahara equation posed on the right and left half-lines. We prove the local well-posedness in the low regularity Sobolev space. We introduce the Duhamel boundary forcing…
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…
In this paper, we present a novel pseudospectral (PS) method for solving a new class of initial-value problems (IVPs) of time-dependent one-dimensional fractional partial differential equations (FPDEs) with variable coefficients and…
This paper presents an approach to study initial-boundary value (IBV) problems for integrable nonlinear differential-difference equations (DDEs) posed on a graph. As an illustrative example, we consider the Ablowitz-Ladik system posed on a…
We study some functionals associated with a process driven by a fractional boundary value problem (FBVP for short). By FBVP we mean a Cauchy problem with boundary condition written in terms of a fractional equation, that is an equation…