Resonance in Linear Differential Equations and L'Hospital's Rule

Approximately $n$-order linear differential equations

We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Differential Equations and Linear Algebra

where D = d/dt is the basic differentiation operator on functions. (The j-th derivative operator, for j ≥ 1, is Dj , and we consider the identity operator I as D0, since it is standard to regard the zero-th derivative of a function as the function itself: D0(y) = y for all functions y.) We call (1.2) an n-th order linear differential operator since the highest derivative appearing in it is the ...

Linear difference and differential equations

Linear Differential Equations