Given a linear functional system (e.g., an ordinary/partial differential system), Serre’s reduction aims at finding an equivalent linear functional system which contains fewer equations and fewer unknowns. The purpose of this paper is to study Serre’s reduction of underdetermined linear systems of partial differential equations with analytic coefficients whose formal adjoints are holonomic in t...

A model order reduction method for index-2 differential-algebraic equations (DAEs) is introduced, which is based on the intrinsic differential equations and on the remaining algebraic constraints. This extends the method introduced in a previous paper for index-1 DAEs. This procedure is implemented numerically and the results show numerical evidence of its robustness over the traditional methods.

In this paper, we introduce a family of fractional-order Chebyshev functions based on the classical Chebyshev polynomials. We calculate and derive the operational matrix of derivative of fractional order $gamma$ in the Caputo sense using the fractional-order Chebyshev functions. This matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...

This paper presents the use of an iteration method to solve the identifiability problem for a class of discretized linear partial differential algebraic equations. This technique consists in replacing the partial derivatives in the PDAE by differences and analyzing the difference algebraic equations obtained. For that, the theory of discrete singular systems, which involves Drazin inverse matri...

In this paper we present singularly impulsive or generalized impulsive dynamical systems. Dynamics of this system is characterized by the set of differential, difference, and algebraic equations. They represent the class of hybrid systems, where algebraic equations represent constraints that differential and difference equations need to satisfy. Generalized term have as source generalized syste...

In this paper we apply hybrid functions of general block-pulse‎ ‎functions and Legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (FDEs)‎. ‎Our approach is based on incorporating operational matrices of‎ ‎FDEs with hybrid functions that reduces the FDEs problems to‎ ‎the solution of algebraic systems‎. ‎Error estimate that verifies a‎ ‎converge...

Holonomic and Pfaffian nonholonomic systems are dynamical systems whose generalized coordinates and velocities are subject to smooth constraints. These systems are usually described by second order differential equations of motion and algebraic equations of constraint. We present an optimal control formulation for these systems that utilizes the multiplier rule to append both the equations of m...