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This book is devoted to recent developments of linear and nonlinear integral inequalities on time scales. The book is intended for the use in the field of dynamic calculus on time scales, dynamic equation and integral equations on time scales. It is also suitable for graduate courses in the above fields. The book is designed for those who have mathematical background on time scales calculus.

The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques.

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Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided fo...

This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.

This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of ...

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This book encompasses recent developments of variational calculus for time scales. It is intended for use in the field of variational calculus and dynamic calculus for time scales. It is also suitable for graduate courses in the above fields. This book contains eight chapters, and these chapters are pedagogically organized. This book is specially designed for those who wish to understand variational calculus on time scales without having exten...

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided fo...

This book is intended for readers who have had a course in theory of functions, isodifferential calculus and it can also be used for a senior undergraduate course. Chapter One deals with the infinite sets. We introduce the main operations on the sets. They are considered as the one-to-one correspondences, the denumerable sets and the nondenumerable sets, and their properties. Chapter Two introduces the point sets. They are defined as the limit...

Chapter 1 represents a short introduction to the theory of iso-probability theory. They are defined iso-probability measure, iso-probability space, random iso-variable of the first, second, third, fourth and fifth kind, iso-expected values, iso-martingales, iso-Brownian motion, iso-Wiener processes, Paley-Wiener-Zygmund integral, Itôs iso-integral, and they are deducted some of their properties. Chapter 2 is devoted on the iso-stochastic diffe...

This book is intended for readers who have had or currently have a course in difference equations or iso-differential calculus. It can be used for a senior undergraduate course. Chapter 1 deals with the linear first-order iso-difference equations, equilibrium points, eventually equilibrium points, periodic points and cycles. Chapter 2 are introduces iso-difference calculus and the general theory of the linear homogeneous and nonhomogeneous iso...

The 'genious idea' is the Santilli's generalisation of the basic unit of quantum mechanics into an integro-differential operator. This depends on local variables, and it is assumed to be the inverse of the isotopic element (the Santilli isounit). It was believed for centuries that the differential calculus is independent of the assumed basic unit, since the latter was traditionally given by the trivial number 1. Santilli has disproved this bel...

This book introduces the main ideas and fundamental methods of iso-differential calculus for iso-functions of several variables. Introduced are the iso-functions of the first, second, third, fourth and fifth kind, and iso-partial derivatives of the first, second, third, fourth, fifth, sixth and seventh kind. In this book, the main conceptions for multiple, line and surface iso-integrals for iso-functions of several variables are given. The boo...

This book is intended for readers who have had a course in iso-differential calculus and it can be used for a senior undergraduate course. Chapter 1 deals with exact iso-differential equations, while first-order iso-differential equations are studied in Chapter 2 and Chapter 3. Chapter 4 discusses iso-integral inequalities. Many iso-differential equations cannot be solved as finite combinations of elementary functions. Therefore, it is importa...

This book presents an introduction to the theory of partial differential equations(PDEs). The book is suitable for all types of basic courses on PDEs. Chapter 2 is devoted on first order PDEs. They are considered classiffcation of first order PDEs, solvability of quasilinear first order PDEs, the Cauchy problem for quasilinear first order PDEs, the Pfaffan equation and some special systems. In Chapters 3 and 4 are considered the classiffcation...

This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedag...