Alpha Calculus

By: Svetlin G. Georgiev, Muhittin Evren Aydin

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eText | 28 April 2026 | Edition Number 1

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Readers may question why non-Newtonian calculus should be used when Newtonian calculus is already available and many scientists are familiar with it. Alpha Calculus attempts to answer this question. Many other mathematical examples can also be given to demonstrate the advantages of using non-Newtonian calculus, for instance, in interpreting differential equations, proving certain mathematical facts more easily, studying functions with variable physical values, and more.

The use of alternative calculi to Newtonian calculus is interesting not only for mathematicians, but also for researchers in other fields. Specifically, it is known that while stock prices, national populations, electric bills, and river surface areas are measured on exponential scales, the magnitude of an earthquake, sound signal levels, and the acidity of chemicals are measured on logarithmic scales.

This suggests that many physical phenomena in nature are expressed using exponential and logarithmic scales, making it more natural to prefer a calculus based on division and multiplication rather than subtraction and addition. Consequently, this book provides researchers in any field with the opportunity to use a calculus that is compatible with an arithmetic system suited to their work.