Fractional Calculus and Fractional Differential Equations MA 663 (Elective Course for MSc 2nd Yr.  and PhD students)

 

Three one-hour lectures per week: 6 credits

Class Timing: 12:00-12:55, Monday; 12:00-12:55, Tuesday; 11:00-11:55, Friday 

Room Number: 1103

First Day of Instruction: Friday, January 3, 2020

Last day of Instruction: Thursday, April 30, 2020

Course Instructor: Swaroop Nandan Bora

Office: E-306 

Phone: 2604

Email: swaroop@iitg.ac.in

 

Change of time-table: 

 

Classes with Wednesday time table

20 January 2020, Monday

Classes with Friday Time table

 25 February 2020, Tuesday
Classes with Tuesday Time table  12 March 2020, Thursday
Classes with Friday Time table  09 April 2020, Thursday
Classes with Monday Time table  15 April 2020, Wednesday

 

Course Contents:  

 

MA663 Fractional Calculus and Fractional Differential Equations [3-0-0-6] Prerequisites: Nil

Total number of lectures: 40-42

Special functions of fractional calculus: Gamma function, MIttag-Leffler function, Wright function. Fractional derivatives and integrals: Grunwald-Letnikov fractional derivatives, Riemann-Liouville fractional derivatives, geometric and physical interpretation of fractional integration and differentiation, sequential fractional derivatives, properties of fractional derivatives, Laplace, Fourier and Mellin transforms of fractional derivatives.

Linear fractional differential equations: Equation of a general form, existence and uniqueness theorem as a method of solution, dependence of a solution on initial conditions, Laplace transform method, standard fractional differential equations, sequential fractional differential equations. Some methods for solving fractional order equations: Mellin transform, power series, orthogonal polynomials, numerical evaluation of fractional derivatives, approximation of fractional derivatives.

Texts/References:

  1. Basic Theory of Fractional Differential Equations, Y. Zhou, World Scientific, 2014.
  2. Fractional Differential Equations, I. Podlubny, Academic Press, 1998.
  3. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, K.B. Oldham and J. Spanier, Dover Publications, 2006.
  4. An Introduction to the Fractional Calculus and Fractional Differential Equations, K.S. Miller and B. Ross, Wiley-Interscience, 1993.
 

 

Plan of the course:

 

  1. Two quizzes: 28 marks.
  2. Mid semester examination: 27 marks.
  3. End semester examination: 45 marks.

 

Important Dates:

 

*Quiz I: Friday, February 7, 2020 (15 Marks)

Mid Semester Exam: 2-4 PM, Wednesday, March 4, 2020 (27 Marks) - Room 5001 (Core V)

*Quiz II: 1100-1155, Thursday with Friday Time table, April 9, 2020 (13 Marks)  (This date may change)

End Semester Exam: 2-5 PM, Saturday, May 9, 2020 (47 Marks)