Related papers: Study of a nonlinear fractional boundary value pro…
In this work we give an efficient method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of two-point boundary value problems.
We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-infinite…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
In this paper we present a theory for the existence of multiple nontrivial solutions for a class of perturbed Hammerstein integral equations. Our methodology, rather than to work directly in cones, is to utilize the theory of fixed point…
The main objective of this paper is analysis of the initial-boundary value problems for the linear time-fractional diffusion equations with a uniformly elliptic spatial differential operator of the second order and the Caputo type…
In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non--Newtonian coefficient. According to a recently…
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.…
We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and…
In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplacian.
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…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results…
The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the…
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.…
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a…
In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…