Fractional Calculus and Applications
Aviation Science and Technology
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Fractional Calculus and Applications | HVA506 | Elective | Master's degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Serap BULUT
Learning Outcomes of the Course Unit
1) Learn some advanced mathematical knowledge.
2) Know the concept of fractional derivative.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ||
| Learning Outcomes | ||||||||||
| 1 | No relation | No relation | Middle | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | Middle | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
e-course
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Not Required
Course Contents
Gamma function and its properties, Beta function and its properties, Error function and its properties, Mittag-Leffler function and its properties, Hypergeometric function and its properties, Fractional integral, Differentiation and integral, Euler fractional differential operator, Riemann-Liouville fractional differential operator, Caputo fractional differential operator, Comprasion of the Riemann-Liouville and Caputo operators, Relation of the Riemann-Liouville and Caputo operators, Examples, Weyl fractional differential operator and its properties.
Weekly Schedule
1) Gamma function and its properties2) Beta function and its properties
3) Error function and its properties
4) Mittag-Leffler function and its properties
5) Hypergeometric function and its properties
6) Fractional integral, Differentiation and integral
7) Euler fractional differential operator
8) Midterm exam
9) Riemann-Liouville fractional differential operator
10) Caputo fractional differential operator
11) Comprasion of the Riemann-Liouville and Caputo operators
12) Relation of the Riemann-Liouville and Caputo operators
13) Examples
14) Weyl fractional differential operator and its properties
15) Weyl fractional differential operator and its properties
16) Final exam
Recommended or Required Reading
1- A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier.
2- R.A.Z. Daou and X. Moreau, Fractional Calculus Applications, Nova.
Planned Learning Activities and Teaching Methods
1) Lecture
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
40% |
|---|---|
Contribution of Final Examination to Course Grade |
60% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required