Fractal calculus is the simple, constructive, and algorithmic approach to natural processes modeling, which is impossible using smooth differentiable structures and the usual modeling tools such as differential equations. It is the calculus of the future and will have many applications.This book is the first to introduce fractal calculus and provides a basis for the research and development of this framework. It is suitable for undergraduate and graduate students in mathematics and physics who have mastered general mathematics, quantum physics, and statistical mechanics, as well as researchers dealing with fractal structures in various disciplines.

Fractional calculus is the calculus of the future, With it, we can solve problems we couldn't have solved before. It is shown that geometric interpretation of fractional integration is "shadows on the walls" and its physical interpretation is "shadows of the past."It may be important to point out that the first application of fractional calculus was made by Abel(1802-1829) in the solution of an integral equation that arises in the formulation of the tautochronous problem.