A COMPREHENSIVE REVIEW ON FRACTIONAL OPERATORS, WAVELETS, AND THEIR APPLICATIONS

Abstract

In this article, we reviewed some of the widely used fractional operators and wavelets, together with their important applications that appear in physics, biology, engineering, and mathematics. Also, the purpose of this review is to provide the reader a comfortable introduction to fractional integrals and derivatives operators and then link them to each other. These operators provide more accurate descriptions of non-smooth phenomena and capture complex dynamics that traditional calculus may fail to capture. In this work, different fractional operators are defined which highlights their applicability to a wide range of complicated systems and their importance in developing mathematical techniques in several fields. This article also outlines some advantages and disadvantages of employing fractional derivatives.