Differential equations arising in mechanics, physics, engineering, biological sciences, economics, and other fields of sciences may be classified into either linear or nonlinear formulated as initial or boundary value problems. The book focuses on the theory and the application of differential equations that examine the state of the art, identify emerging trends, and suggest future directions for developing fields. This book is addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.