dc.contributor.advisor |
Fernandez, Arran (Co-Supervisor) |
|
dc.contributor.advisor |
Özarslan, Mehmet Ali (Supervisor) |
|
dc.contributor.author |
Malyalı, Duygu |
|
dc.date.accessioned |
2023-08-31T12:23:02Z |
|
dc.date.available |
2023-08-31T12:23:02Z |
|
dc.date.issued |
2020-01 |
|
dc.date.submitted |
2020-01 |
|
dc.identifier.citation |
Malyalı, Duygu. (2020). (p,q)-Hahn Difference Operator. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus. |
en_US |
dc.identifier.uri |
http://hdl.handle.net/11129/5723 |
|
dc.description |
Master of Science in Mathematics. Institute of Graduate Studies and Research. Thesis (M.S.) - Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2020. Co-Supervisor: Asst. Prof. Dr. Arran Fernandez and Supervisor: Prof. Dr. Mehmet Ali Özarslan. |
en_US |
dc.description.abstract |
ABSTRACT: One of the main starting point for the theory of calculus is the differentiation operation, which is defined as follows. Firstly, divide the difference of two function values by the difference of the corresponding two arguments, and then take the limit as the two
arguments converge to each other. The result of this limit is called the derivative of the
original function. Many variants of this basic operation have been proposed, giving rise to different theories and types of calculus. In this thesis, I will study some particular variants in which the limiting process is omitted but the two arguments in the quotient expression
are linear functions of each other. The most basic one is the q-calculus (or quantum
calculus), which is a particular case of both the (q,ω)-calculus (or Hahn calculus) and
the (p,q)-calculus, which are the both special cases of the new type called (p,q)-Hahn calculus. These approaches give more discrete theories than the original calculus, more
applicable to quantum physics. But a lot of the structure remains the same: in all
cases there are derivatives, integrals, product and chain rules, exponential and Appell
functions. In this thesis, I will study important properties and special functions
associated with each of these three known types of calculus, and finally, I introduce
the new (p,q)-Hahn Calculus. Keywords: q-calculus or quantum calculus, q,ω-calculus or Hahn Calculus, (p,q)-calculus, (p,q)-Hahn Calculus, Exponential Functions, Appell Polynomials. |
en_US |
dc.publisher |
Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ) |
en_US |
dc.rights |
info:eu-repo/semantics/openAccess |
en_US |
dc.subject |
Mathematics Department |
en_US |
dc.subject |
Calculus |
en_US |
dc.subject |
q-calculus or quantum calculus, q,ω-calculus or Hahn Calculus, (p,q)- calculus, (p,q)-Hahn Calculus, Exponential Functions, Appell Polynomials |
en_US |
dc.title |
(p,q)-Hahn Difference Operator |
en_US |
dc.type |
masterThesis |
en_US |
dc.contributor.department |
Eastern Mediterranean University, Faculty of Arts and Sciences, Department of Mathematics |
en_US |