Introduction to Fractional Calculus

Scientists and engineers have always sought different approaches when it comes to studying and modeling natural phenomena. After all, this is how academics study nature. Fractional calculus is one of the old mathematical methods that was developed long time ago, but was awaken recently. It covers fractional derivative and fractional antiderivative. In this paper, we introduce the basic properties of fractional calculus along with examples. We will review the mathematical derivations and will show where and where not fractional calculus agrees with ordinary derivatives. We proceed to show product rule, quotient rule, and chain rule, to list a few, emerge as examples where fractional and ordinary derivatives tend to depart. Nonetheless, fractional calculus can still be appealing to engineers and the scientific community.