Theory and Methods of Piecewise Defined Fractional Operators (Paperback) (ISBN-13: 9780443221569)

Theory and Methods of Piecewise Defined Fractional Operators introduces new mathematical methods to derive complex modeling solutions with stability, consistency, and convergence. These tools include new types of non-local derivatives and integrals, such as fractal-fractional derivatives and integrals. Drs. Atangana and Araz present the theoretical and numerical analyses of the newly introduced piecewise differential and integral operators where crossover behaviors are observed, as well as their applications to real-world problems. The book contains foundational concepts that will help readers better understand piecewise differential and integral calculus and their applications to modeling processes with crossover behaviors. Several Cauchy problems with piecewise differential operators are considered, and their existence and uniqueness under some conditions are presented; in particular, the Carathéodory principle is used to ensure the existence and uniqueness of these new Cauchy problems. New numerical schemes are introduced to derive numerical solutions to these new equations, and the stability, consistency, and convergence analysis of these new numerical approaches are also presented.

Author: Abdon Atangana,Seda İğret Araz
ISBN-10: 0443221561
ISBN-13: 9780443221569
Publisher: Morgan Kaufmann Publishers
Language: English
Published: 12/01/2026
Pages: 260
Format: Paperback