1,832 Results Found

Under suitable continuity and uniqueness conditions, solutions of an $\alpha$ order Caputo fractional boundary value problem are differentiated with respect to boundary values and boundary points. This extends well-known results for nth order boundary...

In this paper, we study inverse nodal problems for a boundary value problem. A uniqueness result for the potential function and a reconstruction method are obtained. By using the nodal points as input data, we compute the approximation solution of th...

In the numerical integration of the second-order nonlinear boundary value problem (BVP), the right boundary condition plays the role as a target equation, which is solved either by the half-interval method (HIM) or a new derivative-free Newton method...

In this paper, the time-independent Klein-Gordon equation in ${\mathbb{R}}^3$ is treated with a decomposition of the operator $\Delta -{\gamma }^{2}I$ by the Clifford algebra $Cl\left(V_{3,3}\right)$. Some properties of integral operators associated the kind of equations and some...

In this paper, the upper and lower solution method is proposed in order to solve the second order interval boundary value problem. We study first a class of linear interval boundary value problems and then investigate a class of nonlinear interval bo...

In this work, we study stochastic boundary value problems that arise in acoustics and linear elasticity via a Wiener chaos expansion. In particular, for both cases, we provide the appropriate variational formulation for the stochastic-source Helmholt...

The generalized monotone iterative technique for sequential $2q$ order Caputo fractional boundary value problems, which is sequential of order q, with mixed boundary conditions have been developed in our earlier paper. We used Green’s fu...

We consider a non-standard nonlinear singularly perturbed 2D initial-boundary value problem with Venttsel type boundary conditions, arising in homogenization of radiative-conductive heat transfer problems. We establish existence, uniqueness and regul...

We study a boundary value problem for nonlinear partial differential equations of the hyperbolic type on the plain in a domain with a complex boundary. To find the missing data for the given boundary constraints, we solve a supplementary nonlinear pr...

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued...

In this paper, we use the modified decomposition method for solving the system of third-order nonlinear boundary value problems associated with obstacle problems. Some examples of system of third-order nonlinear boundary value problems are given. The...

A nonlinear transformation from the solution of linear KdV equation to the solution of Sharma-Tasso-Olver (STO) equation is derived out by using simplified homogeneous balance (SHB) method. According to the nonlinear transformation derived here, the...

We give a definition of Green’s function of the general boundary value problems for non-self-adjoint second order differential equation with involution. The sufficient conditions for the basis property of system of eigenfunctions are established in t...

Sufficient conditions are obtained for a signed maximum principle for boundary value problems for Riemann–Liouville fractional differential equations with analogues of Neumann or periodic boundary conditions in neighborhoods of simple eigenvalu...

Ulam type stability is an important property studied for different types of differential equations. When this type of stability is applied to boundary value problems, there are some misunderstandings in the literature. In connection with this, initia...

In this paper, we discuss the existence of solutions for a hybrid boundary value problem of Caputo fractional differential equations. The main tool used in our study is associated with the technique of measures of noncompactness. As an application, w...

In this paper, the solvability of a system of nonlinear Caputo fractional differential equations at resonance is considered. The interesting point is that the state variable $x\in {\mathbb{R}}^n$ and the effect of the coefficient matrices matrices B and C of bou...

This paper deals with Lopatinskii type boundary value problem (bvp) for the (poly) harmonic differential operators. In the case of Robin bvp for the Laplace equation in the ball $B_1$ a Green function is constructed in the cases $c>0$, $c\notin -\mathbf{N}$...

A boundary value problem for Hadamard fractional differential equations of variable order is studied. Note the symmetry of a transformation of a system of differential equations is connected with the locally solvability which is the same as the exist...

A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case) is proposed. It is shown that other definitions worked out in order to find Lie...

This paper proposes a novel numerical approach for handling fractional boundary value problems. Such an approach is established on the basis of two numerical formulas; the fractional central formula for approximating the Caputo differentiator of orde...

In this paper, we study the solvability of various two-point boundary value problems for $x^{\left(4\right)}=f(t,x,x^{\prime },x^{″},x^{‴}),t\in (0,1),$ where f may be defined and continuous on a suitable bounded...

The boundary shape function method (BSFM) and the variational iteration method (VIM) are merged together to seek the analytic solutions of nonlinear boundary value problems. The boundary shape function method transforms the boundary value problem to...

It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: $\mathcal{C}=\{(n,k):0\le k\le n,k\in {\mathbb{N}}_0,n$...

In this paper, we study the existence and multiplicity of solutions for the discrete Dirichlet boundary value problem of the Kirchhoff type, which has a symmetric structure. By using the critical point theory, we establish the existence of infinitely...

In this study, a high-order compact finite difference method is used to solve boundary value problems with Robin boundary conditions. The norm is to use a first-order finite difference scheme to approximate Neumann and Robin boundary conditions, but...

In this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain so...

In this paper, we find the solutions of fourth order fractional boundary value problems by using the reproducing kernel Hilbert space method. Firstly, the reproducing kernel Hilbert space method is introduced and then the method is applied to this ki...

In this present paper, we study the difference method for solving a boundary value problem of the Caputo type q-fractional differential equation. This method is based on the numerical quadrature of the q-fractional derivative and the q-Taylor expansi...

Recently, it was observed that the concentration/heat transfer of pure/nano fluids are finally governed by singular second-order boundary value problems with exponential coefficients. These coefficients were transformed into polynomials and therefore...

Our goal is to address the question of existence and uniqueness of a positive continuous solution to some semipositone fractional boundary value problems on the half-line. Global estimates on this solution are given. This kind of problems, where the...

Under barrier strips type assumptions we study the existence of $C^3[0,1]$ —solutions to various two-point boundary value problems for the equation $x^{‴}=f(t,x,x^{\prime },x^{″}).$ We give also some...

In this article, we present a two-point boundary value problem with separated boundary conditions for a finite nabla fractional difference equation. First, we construct an associated Green’s function as a series of functions with the help of spectral...

This article investigates certain fixed-point results enjoying nonlinear almost contraction conditions in the setup of relational metric space. Some examples are constructed in order to indicate the profitability of our results. As a practical use of...

The current manuscript introduces an efficient modification scheme, based on the Adomian decomposition method, for the numerical solution of systems of two-point boundary-value problems. Indeed, this introduced method is characterized by high computa...

In this paper, we investigate positive solutions of boundary value problems for a general second-order nonlinear difference equation, which includes a Jacobi operator and a parameter $\lambda$. Based on the critical point theory, we obtain the existen...

This paper provides a method to bound and calculate any eigenvalues and eigenfunctions of n-th order boundary value problems with sign-regular kernels subject to two-point boundary conditions. The method is based on the selection of a particular type...

This paper is a survey of the recent results of the author for various classes of boundary value problems for Hilfer fractional differential equations and inclusions of fractional order in $(1,2]$ supplemented with different kinds of nonlocal boundary...

This paper is concerned with multiple solutions for a class of nonlinear fourth-order boundary value problems with parameters. By constructing a special cone and applying fixed point index theory, the multiple solutions for the considered systems are...

Determining constitutive model parameters from in situ tests offers several advantages, including reduced time, lower cost, and minimal soil disturbance. As part of a research project, an automated framework was developed to derive constitutive model...

In this paper, we studied the existence results for solutions of a new class of the fractional boundary value problem in the Caputo–Hadamard settings. Moreover, boundary conditions of this fractional problem were formulated as the mixed multi-order H...

In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of first order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocat...

In this paper, the sinc-derivative collocation approach is used to solve second order integro-differential boundary value problems. While the derivative of the unknown variables is interpolated using sinc numerical methods, the desired solution and t...

In this paper, the Sinc-derivative collocation method is used to solve linear and nonlinear multi-point boundary value problems. This is done by interpolating the first derivative of the unknown variable via Sinc numerical methods and obtaining the d...

In this paper, an accurate and fast algorithm is developed for the solution of tenth order boundary value problems. The Haar wavelet collocation method is applied to both linear and nonlinear boundary value problems. In this technqiue, the tenth orde...

In the present research, single and multi-valued (k,ψ)-Hilfer type fractional boundary value problems of order in (1,2] involving nonlocal integral boundary conditions were studied. In the single-valued case, the Banach and Krasnosel’ski...

This paper aims to investigate a class of fractional multi-point boundary value problems at resonance on an infinite interval. New existence results are obtained for the given problem using Mawhin’s coincidence degree theory. Moreover, two exam...

In this paper, an efficient computational discretization approach is investigated for nonlinear fourth-order boundary value problems using beam theory. We specifically deal with nonlinear models described by fourth-order boundary value problems. The...

The authors investigate Langevin boundary value problems containing a variable order Caputo fractional derivative. After presenting the background for the study, the authors provide the definitions, theorems, and lemmas that are required for comprehe...