Geometric reduction methods for differential-algebraic equations (DAEs) aim at an iterative reduction of the problem to an explicit ODE on a lower-dimensional submanifold of the so-called semistate space. This approach usually relies on certain algebraic (typically constant-rank) conditions holding at every reduction step. When these conditions are met the DAE is called regular. We discuss in t...

In this note we show that the example presented in a recent paper by Ghazanfari et al. is incorrect. Namely, the " exact solution " suggested by the authors is not solution of the given fuzzy differential equation (FDE). Indeed, the authors have proposed an exact solution which is independent from the initial condition. So, we obtain the correct exact solution using the characterization theorem...

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

In this paper, firstly, we gain some basic properties and characterization theorems of the differential and local sub-differential of the fuzzy mapping, obtain an important result that the local sub-differential of fuzzy mapping is an empty set or a convex set. Secondly, we generalize the concept of local differentiability of fuzzy mapping, and obtain some basic properties about the concept. At...

In this paper, we use the generalized differentiability concept tostudy the fuzzy transport equation. We consider transport equationin the homogeneous and non-homogeneous cases with fuzzy initialcondition. We also present the solution when speed parameter is a fuzzynumber. Our method is based on the construction of the solutionsby employing Zadeh's extension principle.

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

fuzzy control systems have had various applications in a wide range of science and engineering in recent years. since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). conceptually, there are two types of stability for control systems: lyapunov stability (a special case ...

Spend your few moment to read a book even only few pages. Reading book is not obligation and force for everybody. When you don't want to read, you can get punishment from the publisher. Read a book becomes a choice of your different characteristics. Many people with reading habit will always be enjoyable to read, or on the contrary. For some reasons, this computer methods for ordinary different...