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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.