Conformable Fractional Differential Operators With Applications

Abstract

A fractional differential operator Dα has a conformable property if Dα (t) → f ′ (t) when α → 1. So fractional calculus is a generalization of the classical one. Hence many results and properties in classiborrowersulus are studied and generalized in the fractional case. In this thesis, we study many fractional derivatives that are based on the limit definition, and in the particular conformable fractional derivative is considered as it is the most popular definition used in the literature. Its main results and properties are reviewed and summarized. In addition, many applications for different types of fractional differential equations are provided. Moreover, we study three specific fractional differential operators. In particular, the UD-fractional derivative, the Exponential fractional derivative, and the Hyperbolic fractional derivative are introduced. In each one, the main properties and results are investigated and proved. As applications, various kinds of fractional differential equations based on these fractional operators are considered and solved.