Krein [1] mentioned that for each PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. They claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. They have only considered lo...

Abstract Hybrid Boundary Value Method (HyBVM) is a new scheme, which based on Linear Multistep (LMM). The HyBVM the hybrid version of Methods (BVMs) are methods derived to overcome limitations LMMs. This scheme shares same characteristic with Runge Kutta method as data utilized at off-step points. In this work, we apply two second order Problems (BVPs) mixed boundary conditions and results effi...

we consider a mixed boundary value problem for a quarter-plane with a robin condition on one edge. we have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.

abstract.   the sturm-liouville boundary value problem of the multi-order fractional differential equation  is studied. results on the existence of solutions are established. the analysis relies on a weighted function space and a fixed point theorem. an example is given to illustrate the efficiency of the main theorems.