Higher-order Cahn–Hilliard equations with dynamic boundary conditions

Higher order multi-point fractional boundary value problems with integral boundary conditions

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Damped Wave Equations with Dynamic Boundary Conditions

We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their wellposedness and describe some qualitative properties of their solutions, including boundedness, stability, or almost periodicity. In particular, we are able to characterize the analyticity of ...

Multiple monotone positive solutions for higher order differential equations with integral boundary conditions

where n ≥ , f : [, ]× (R+)n– → R+ is continuous in which R+ = [,+∞), A and B are right continuous on [, ), left continuous at t = , and nondecreasing on [, ], withA() = B() = ; ∫   v(s)dA(s) and ∫   v(s)dB(s) denote the Riemann-Stieltjes integrals of v with respect to A and B, respectively. Boundary value problems (BVPs for short) for nonlinear differential equations arise in m...

Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions

In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...

Collocation for High-Order Differential Equations with Lidstone Boundary Conditions