Advanced calculus is a branch of mathematics that extends the concepts of calculus to higher dimensions and more complex functions. It encompasses topics such as vector calculus, differential equations, and real analysis. The book covers a diverse range of topics within advanced calculus. The chapters touch upon subjects a collection of research papers, articles, or lecture notes on various advanced calculus subjects. Each topic is a specific research area or field of study within advanced calculus. The book is likely aimed at researchers, graduate students, and academics who are well-versed in advanced calculus and seeking in-depth insights into specialized areas of the subject. The topics covered in the book, such as Fractional Asset Flow Differential Equations, Nonlinear Gronwall–Bellman Type Inequalities, Time Automorphisms on C*-Algebras, and Rational functions as new variables. It may also be of interest to researchers and professionals working in these fields who wish to deepen their understanding of advanced calculus concepts and their applications.