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.

In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the...

We describe a fortran collocation boundary value problem solver in the COLSYS family of codes, for state-dependent delay and advanced-delay differential equation BVPs. Advanced-delay problems arise in a number of applications, including as the defining equations for travelling waves on a lattice. At first sight, since we solve all the equations in one go, advanced terms create no more difficult...

In chemical engineering, several processes are represented by singular boundary value problems. In general, classical numerical methods fail to produce good approximations for the singular boundary value problems. In this paper, Chebyshev finite difference (ChFD) method and DTM-Pad´e method, which is a combination of differential transform method (DTM) and Pad´e approximant, are applied for sol...

Because of applications in physics, bioscience, epidemiology and so on, most literature about differential equations with delay has focused on existence of periodic solution, oscillation, and so on. In recent years, there has been increasing interest in boundary value problems for differential equations with delay, see for example 1–8 . By using fixed-point theorems, the authors discussed the e...