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bubblewrap said:What happens when##\mu## is not 1? I don't understand how this is used. For example when ##\mu## is 2, does it mean that you use ##e## defined in ##E^t_\mu##? What does that mean though?
bubblewrap said:Yeah but as I said what happens when mu is not 1, other than it not being ##e^t##?
Fractional calculus is a branch of mathematics that deals with generalizing the traditional concepts of differentiation and integration to non-integer orders. It involves the study of fractional derivatives and integrals, which are defined for non-integer orders of differentiation or integration.
Fractional calculus has many applications in physics, engineering, economics, and other fields. Some common applications include modeling of non-Newtonian fluids, signal processing, and control theory. It can also be used to solve certain types of differential equations that cannot be solved using traditional methods.
The main difference between fractional calculus and traditional calculus is that fractional calculus deals with differentiation and integration of non-integer orders, while traditional calculus only deals with integer orders. Additionally, fractional calculus involves the use of fractional derivatives and integrals, which have different properties compared to traditional derivatives and integrals.
Fractional calculus can be challenging to understand for those who are not familiar with it. However, with the right resources and guidance, it can be learned and applied effectively. It is important to have a strong understanding of traditional calculus before delving into fractional calculus.
Studying fractional calculus can provide a deeper understanding of traditional calculus and its applications. It also allows for the modeling and analysis of systems that cannot be described by traditional calculus. Additionally, fractional calculus has practical applications in various fields, making it a valuable skill for scientists and researchers.