Bøger af Abdon Atangana

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.

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.