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Abstract

This paper presents a review of brief introduction to fractional calculus with the definitions of fractional derivatives and operators. Its properties and useful mathematical functions are specified. The fractional derivatives importance is seen in many fields and can be used in modeling various phenomena. The types of fractional derivatives are being added and focus is made on caputo derivatives with its usage in latest researches. Its merits and demerits are stated which give insight to understand caputo derivatives more effectively. This understanding will help generate and solve new problems arising in various fields such as mathematical physics, dynamical systems, fluid mechanics, statistics, biology, viscoelasticity and many more. The caputo derivative examples of some functions are listed in tabular form. The difference and comparison between two types of fractional derivatives namely, Riemann-Liouville and caputo derivatives are given. The highlighted portion is the latest research and problem solving made in different areas using caputo derivatives.