Inequalities are a great tool in mathematics and a core concept in nearly every area of pure and applied mathematics. The relevance of the term lies in its emerging technical adoption for multiple applications, from research to applications. Here, we will derive and establish the new inequalities in which further inequalities will immediately follow from it, and will be essentially related to a fractional derivative and integral of a function with respect to another function. The concept of these operators introduced in this book as global fractional differential and integral operators provides a generalized structure of analysis.