In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

There are many routines developed for solving ordinary differential Equations (ODEs) of different types. In the case an nth-order ODE that admits r-parameter Lie group (3≤r≤n), there is a powerful method symmetry analysis by which reduced to (n−r)th-order plus r quadratures provided algebra formed infinitesimal generators solvable. It would seem this not widely appreciated and/or used as it men...

This paper is devoted to the derivation of expansion and sampling theorems associated with nth order discontinuous eigenvalue problems defined on [−1, 1], illustrated with detailed examples. The problem consists of nth order differential expressions and n boundary and n compatibility conditions at x = 0. The differential expressions are defined, in general, in two different ways throughout [−1,...

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients. 1. Background on counting zeros of solutions of linear ordinary differential equations 1.1. De la Valée Poussin theorem and Novikov’s counterexample. A linear...

had been investigated. As it is noted here, these equations are not adjoint equations and are referred to as quasi-adjoint equations. Equation (E) is a special case of linear nth-order difference equations with quasi-differences. Such equations have been widely studied in the literature, see, for example, [6, 11] and the references therein. The natural question which arises is to find the adjoi...

We are concerned with proving that solutions of certain dynamical systems on time scales satisfy some monotoneity conditions. These results then give important results for nth order linear scalar equations. We then give a related result for a third order nonlinear (Emden–Fowler type) dynamic equation.