A function can be differentiated to the 1st or 2nd order (generally to the nth order where n is a Natural number) by using the notion of ordinary Calculus and the results obtained thereof also lead to exclusive deductions. Naturally, a question arise that the same function can be differentiated to, say, 1/2 nd order? Or can we deduce significant results from the acquired information, by using fractional calculus, that may not be achieved through ordinary calculus. In this presentation, an attempt will be made to offer basic notions of fractional calculus followed by the description of techniques that are utilized to determine the analytical and numerical solutions of fractional differential equations. To be specific, we will discuss the modeling of viscoelastic fluid by using the aforesaid effective tool. Lastly, followed by a transient literature review, the intensification of heat transfer of hybrid nanofluid is being investigated by utilizing a fractional model and a comparative analysis between the experimental data and existing models is also offered. It is established that the results obtained through the fractional model are in good agreement with experimental data and it can be a potential substitute of the existing models.