Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
FMA727-13	FRACTIONAL INTEGRAL I	Compulsory	1	1	6

Level of Course Unit

Third Cycle

Objectives of the Course

Teaching high level of mathematics to Phd. students.

Name of Lecturer(s)

Doç.Dr. Erhan SET

Learning Outcomes

1	Students who successfully complete this course: Students will learn theoretical concepts in mathematics and how to read academical journals.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Riemann-Liouville Fractional Integrals and Derivatives, The Abel integral equation, On the solvability of the Abel equation in the space of integrable functions, Fractional integrals and derivatives of complex order, Fractional integrals of some elementary functions, The Fractional Integrals of Hölder and Summable Functions, Mapping properties in the space ,Mapping properties in the space , The Main Properties of Fractional Integrals and Derivatives, Definitions and elementery properties, Fractional integrals of Hölderian functions, Fractional integrals of summable functions, Representation of Function by Fractional Integrals of -Function, Inversion of fractional integrals of -Function

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Riemann-Liouville Fractional Integrals and Derivatives
2	The Abel integral equation
3	On the solvability of the Abel equation in the space of integrable functions
4	Fractional integrals and derivatives of complex order,
5	Fractional integrals of some elementary functions,
6	The Fractional Integrals of Hölder
7	Mapping properties in the space H^lamda ,
8	midterm
9	Mapping properties in the space L^p,
10	The Main Properties of Fractional Integrals
11	The Main Properties of Fractional Derivatives,
12	Fractional integrals of Hölderian functions
13	Fractional integrals of summable functions
14	Representation of Function by Fractional Integrals of L^p -Function
15	Inversion of fractional integrals of L^p -Function
16	Final exam

Recommended or Required Reading

Samko, S.G., Kilbas, A.A., and Marichev, O.I., Fractional Integrals and Derivatives. 1993

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Attending Lectures	14	4	56
Self Study	14	6	84
Individual Study for Mid term Examination	1	18	18
Individual Study for Final Examination	1	18	18
TOTAL WORKLOAD (hours)			180

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	4	5	3	5	4	4	4

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High