A class of related Dirichlet and initial value problems

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

A novel technique for a class of singular boundary value problems

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

Existence of positive solution to a class of boundary value problems of fractional differential equations

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

Some Properties of Solutions to a Class of Dirichlet Boundary Value Problems

and Applied Analysis 3 We denote by ∧l ∧l R the space of l-covectors in R and the direct sum ∧ R n ⊕ l 0 ∧l R 2.1 is a graded algebra with respect to the wedge product ∧. We will make use of the exterior derivative: d : C∞ ( Ω,∧l ) −→ C∞ ( Ω,∧l 1 ) 2.2 and its formal adjoint operator d∗ −1 nl 1 ∗ d∗ : C∞ ( Ω,∧l 1 ) −→ C∞ ( Ω,∧l ) , 2.3 known as the Hodge codifferential, where the symbol ∗ denot...

On the existence of nonnegative solutions for a class of fractional boundary value problems

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...