Fractional Differential Equations
Mathematics
Institute of Natural and Applied Sciences
Third Cycle (Doctorate Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Fractional Differential Equations | MAT629 | Elective | Doctorate degree | 1 | Spring | 8 |
Name of Lecturer(s)
Associate Prof. Dr. Mine Aylin BAYRAK
Learning Outcomes of the Course Unit
1) Reveal the difference between of Classic-order derivative-integral and fractional-order derivative-integral.
2) Calculate the fractional order derivatives and integrals of a function.
3) Interpret fractional calculus in different areas and make the applications in this areas.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Differential equations
Course Contents
A brief history of fractional calculus, classical-order integration and differentiation, Special Functions of fractional calculus . Grünwald-Letnikov fractional derivative and integral. Riemann - Liouville fractional derivative and integral. Caputo fractional derivative and integral.Properties of fractional derivative. Fractional Ordinary Differential Equations and Applications. Fractional Partial Differential Equations and Applications. Other Applications of Fractional Calculus In Mathematics. Engineering Applications of Fractional Calculus.
Weekly Schedule
1) A brief history of fractional calculus.2) Classical-order integration and differentiation.
3) Special Functions of fractional calculus.
4) Special Functions of fractional calculus.
5) Grünwald-Letnikov fractional derivative and integral.
6) Grünwald-Letnikov fractional derivative and integral.
7) Riemann - Liouville fractional derivative and integral.
8) Riemann - Liouville fractional derivative and integral.
9) Caputo fractional derivative and integral.
10) Properties of fractional derivative
11) Fractional Ordinary Differential Equations and Applications.
12) Fractional Ordinary Differential Equations and Applications.
13) Fractional Partial Differential Equations and Applications.
14) Fractional Partial Differential Equations and Applications.
15) exam
16) exam
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
1) Drill and Practice
2) Modelling
3) Group Study
4) Brain Storming
5) Lab / Workshop
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
30% |
|---|---|
Contribution of Final Examination to Course Grade |
70% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required