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.
Les mer
1. Piecewise differential operators and their properties2. Piecewise integral operators and their properties3. Existence and uniqueness of Cauchy problems with nonlocal operators under the framework of Carathéodory’s4. Extension of second-order parametrized Runge-Kutta method to ODE with nonlocal operators 5. Existence, uniqueness, and numerical analysis of piecewise IVP with classical and global differentiation6. Theoretical and numerical analysis of piecewise IVP with classical and fractional derivative7. Analysis of piecewise deterministic and stochastic Cauchy problems 8. Numerical analysis of piecewise Cauchy problem with fractional and global derivative 9. Analysis of a deterministic-fractional stochastic Cauchy problem 10. Analysis of piecewise Cauchy problem with global and fractal-fractional derivative11. Analysis of piecewise Cauchy problem with global and stochastic12. Piecewise fractal-fractional: Theoretical and numerical analysis
Les mer
Presents the theoretical and numerical analyses of the newly introduced piecewise differential and integral operators where crossover behaviors are observed
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
Includes definitions of derivatives and integrals with their different properties
Presents theoretical and numerical analyses of newly introduced piecewise
Covers differential and integral operators where crossover behaviors are observed
Les mer
Produktdetaljer
ISBN
9780443221569
Publisert
2024-07-01
Utgiver
Vendor
Morgan Kaufmann Publishers In
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
260
Forfatter