Golmankhaneh A. Fractal Calculus and Its Applications. Fα-calculus 2023

Textbook in PDF format

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.
Introduction to Analysis of Fractals
Basic Tools
Fractal Cantor Like Sets
Fractal Calculus
Local Fractal Differential Equations
Stability of Fractal Differential Equations
Generalization of Fractal Calculus
Applications of Fractal Calculus
Appendix
Bibliography
Index