Series solutions of coupled differential equations with one regular singular point

Formal series solutions of singular systems of linear differential equations and singular matrix pencils

A system of n linear differential equations xy'{x) =x~8B{x)y(x) is considered, in which s is a positive integer and B(x) is a formal power series. In a preceding paper [6] the author has developed a method for evaluating a formal fundamental matrix solution to the system. This method leads to the algebraic treatment of certain singular matrix pencils. In the present paper the author provides so...

New explicit and Soliton Wave Solutions of Some Nonlinear Partial Differential Equations with Infinite Series Method

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...

Series solutions to a second order linear differential equation with regular singular points

for values of x > 0. For values of x < 0, if r is an integer then one can employ the solution given by eq. (2) without modification. If r is not an integer, then one can obtain the solution from eq. (2) by analytic continuation in the complex plane. In particular, for non-integer r there is a branch point at x = 0 and it is convenient to choose the branch cut to lie along the negative real axis...

On Six Solutions for m-Point Differential Equations System with Two Coupled Parallel Sub-Super Solutions

Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.