Applications of Piecewise Defined Fractional Operators, Volume Two 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 newly introduced piecewise differential and integral operators where crossover behaviors are observed, along with applications. The book contains foundational concepts that will help readers better understand piecewise differential and integral calculus and their applications to modeling processes. Concepts are applied to heat transfer, groundwater transport, groundwater flow, telegraph dynamics, heart rhythm, and others. Applying principles introduced in the first volume, 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 presented.

• Provides in-depth explanation of differential equations with fractional and piecewise differential and integral operators
• Helps readers understand why the concept of piecewise calculus is needed
• Presents definitions of derivatives and integrals with their different properties
• Volume 2 provides a variety of real-world applications including chaos, epidemiological modeling, biological modeling, and others in the case of ordinary differential equations, as well as problems arising from heat transfer, groundwater transport, groundwater flow, telegraph dynamics, and others