Snezhana Hristova

The main aim of the book is suggesting and application in an appropriate computer environment of some approximate methods for solving different types of differential equations such as differential equations with a special type of delay, difference equations and Caputo fractional differential equations. The main characteristic of these methods is the approximate obtaining of the exact solution as a limit of monotonic sequences of successive approximations. The suggested methods are based on the application of upper and lower solutions to the studied problems. Several algorithms are theoretically proved and practically applied for approximately solving of various types of equations. Much of the material presented in this book is based on the recent research of authors on the topic. The current book is intended for a wide audience, including Mathematicians, Applied Researchers, Computer Scientists and Practitioners, whose interest extends beyond the boundaries of qualitative analysis of differential equations and the way to solve equations approximately.

The main aim of the book is to present various types of neural networks and their stability properties illustrated by simulations. It is given several discrete models such as Hopfield-type delay impulsive neural networks, neural networks with non-instantaneous impulses and delays, and several continuous neural networks with switching topologies at impulsive times both deterministic as well as random. It is discussed different types of stability properties of the considered models. Also, it is studied the leader-following consensus problem for discrete multi-agent system with non-instantaneous impulses. Most of the theoretical results are illustrated by computer simulations. The study in the book is motivated by the potential applications of neural networks. It required the definitions and study of models which can more adequate describe the behavior in multi-agent systems. Much of the material presented in this book is based on the recent research of authors on the topic. The current book is intended for a wide audience, including Mathematicians, Applied Researchers, and Practitioners, whose interest extends beyond the boundaries of qualitative analysis of neural networks.

This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses. It aims to equip the reader with mathematical models and theory behind real life processes in physics, biology, population dynamics, ecology and pharmacokinetics. The authors examine a wide scope of differential equations with non-instantaneous impulses through three comprehensive chapters, providing an all-rounded and unique presentation on the topic, including:- Ordinary differential equations with non-instantaneous impulses (scalar and n-dimensional case)- Fractional differential equations with non-instantaneous impulses (with Caputo fractional derivatives of order q ? (0, 1))- Ordinary differential equations with non-instantaneous impulses occurring at random moments (with exponential, Erlang, or Gamma distribution)Each chapter focuses on theory, proofs and examples, and contains numerous graphs to enrich the reader’s understanding. Additionally, a carefully selected bibliography is included. Graduate students at various levels as well as researchers in differential equations and related fields will find this a valuable resource of both introductory and advanced material.

This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses. It aims to equip the reader with mathematical models and theory behind real life processes in physics, biology, population dynamics, ecology and pharmacokinetics. The authors examine a wide scope of differential equations with non-instantaneous impulses through three comprehensive chapters, providing an all-rounded and unique presentation on the topic, including:- Ordinary differential equations with non-instantaneous impulses (scalar and n-dimensional case)- Fractional differential equations with non-instantaneous impulses (with Caputo fractional derivatives of order q ? (0, 1))- Ordinary differential equations with non-instantaneous impulses occurring at random moments (with exponential, Erlang, or Gamma distribution)Each chapter focuses on theory, proofs and examples, and contains numerous graphs to enrich the reader’s understanding. Additionally, a carefully selected bibliography is included. Graduate students at various levels as well as researchers in differential equations and related fields will find this a valuable resource of both introductory and advanced material.