Elements of q-calculus and fractional q-calculus

MAM intensive research course for PhD students and researchers

March  14, 2019, Wednesday, 

 

Lecture 1, 15.15- 16.05, breake 5 minutes, Lecture 2, 16.10-17.00

Location: R2-605, Västerås, Mälardalen University

MAM research frontier lecture series

Intensive PhD course for PhD students and researchers.

Speaker: Professor Predrag Rajković, Department for Mathematics and Informatics, Faculty of Mechanical Engineering, University of Niš, Serbia

Title:

Lecture 1: q-Calculus - from basics to differential and integral operators

Lecture 2: Elements of fractional q-calculus

Abstract:

Lecture 1: q-Calculus - from basics to differential and integral operators

The theory of q-calculus starts with a real parameter q in purpose to define the discrete mathematical objects such that they are connected with well-known mathematical notions. It has its full justification in the fact that many continuous scientific problems have their discrete versions. In accordance to the basics of q-calculus, analogs of the numbers and operations, elementary functions, differential and integral operator, the whole structure of mathematical analysis is developed. In special, we gave contributions in the mean-value theory, q-Taylor formula, integral inequalities. These results are used in considering some new iterative methods for  solving equations and systems. 

Lecture 2: Elements of fractional q-calculus

The fractional calculus is used in various sciences because of its ability to describe memory effects. Today there are a number of concepts with different definitions of fractional integrals and derivatives and their applications in mathematics and other sciences. Several types of fractional q-integral operators and fractional q-derivatives were developed, always with the lower limit of integration equal to zero. However, in some considerations, such as solving of q-differential equation of fractional order with initial values in nonzero point, it is of interest to allow that the lower limit of integration is variable. In our papers, we succeeded to generalize this theory in that direction. We introduced a q-Taylor-like formula which had included fractional q-derivatives of the function. Also, the application of these derivatives to q-exponential functions allowed us to introduce q-analogues of the Mittag-Leffler function. Vice versa, those functions could be used for defining generalized operators in the fractional q-calculus.

Dr  Predrag Rajković, full professor, head of the Department for Mathematics and Informatics, Faculty of Mechanical Engineering, University of Niš, Serbia

Professor Dr Predrag Rajković is a mathematician  doing his research mostly in the Special Functions and Numerical Analysis, but also with contributions in various scientific areas and good cooperation with numerous coauthors. His papers are published in the respectable journals and conference proceedings.  He lectured a lot of different courses at his institution (special functions, numerical analysis, operational research, programming and graphics) and lead young scientists to their thesis.