Course: **Control and optimization for non-local and fractional differential equations**

Period: Summer 2022 (August 1st – August 12nd, 2022)

#### I. Introduction to Control Theory

• Lecture 1: **Introduction to Control Theory**

• Lecture 2: **Introduction to Control Theory**

#### II. Non-local in time models

• Lecture 3: **ODE and ODE with memory**

• Lecture 4: **Fractional calculus and fractional-in-time ODE and PDE**

• Lecture 5: **Control theory for fractional-in-time ODE and PDE**

#### III. Non-local in space models

• Lecture 6: The fractional Laplacian

• Lecture 7: **The fractional Laplacian in non-local PDE** || Lecture 8: **The fractional Laplacian in non-local PDE**

• Lecture 9: Control theory for PDE involving the fractional Laplacian || Lecture 10: **Control theory for PDE involving the fractional Laplacian**

#### IV. Numerical approximation of PDE and numerical control

• Lecture 11: **Introduction to the numerical approximation of PDE and numerical control**

• Lecture 12: **Introduction to the numerical approximation of PDE and numerical control**

• Lecture 13: **Numerical approximation and control of wave equations**

• Lecture 14: **Numerical approximation and control of fractional PDE**

#### V. Complementary topics

• Lecture 15: **Turnpike Theory**

• Lecture 16: **PDE with non-local integral kernels**