Numerical Methods for Fractal-Fractional Differential Equations and Engineering

1. Basic principle of nonlocalities. 2. Basic of fractional operators. 3. Definitions of fractal-fractional operators with numerical approximations. 4. Error analysis. 5. Existence and uniqueness of fractal fractional differential equations. 6. A numerical solution of fractal-fractional ODE with linear interpolation. 7. Numerical scheme of fractal-fractional ODE with middle point interpolation. 8. Fractal-Fractional Euler method. 9. Application of fractal-fractional operators to a chaotic model. 10. Fractal-fractional Modified Chua chaotic attractor. 11. Application of fractal-fractional operators to study a new chaotic model. 12. Fractal-fractional operators and their application to a chaotic system with sinusoidal component. 13. Application of fractal-fractional operators to four-scroll chaotic system. 14. Application of fractal-fractional operators to a novel chaotic model. 15. A 4D chaotic system under fractal-fractional operators. 16. Self-excited and hidden attractors through fractal-fractional operators. 17. Dynamical analysis of a chaotic model in fractal-fractional operators. 18. A chaotic cancer model in fractal-fractional operators. 19. A multiple chaotic attractor model under fractal-fractional operators. 20. The dynamics of multiple chaotic attractor with fractal-fractional operators. 21. Dynamics of 3D chaotic systems with fractal-fractional operators. 22. The hidden attractors model with fractal-fractional operators. 23. An SIR epidemic model with Fractal-fractional derivative. 24. Application of fractal-fractional operators to COVID-19 infection.