Quantum Calculus and Its Applications in Geometric Function Theory

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Guest Editors

Prof. Hari Mohan Srivastava
University of Victoria, Victoria, British Columbia V8W 3R4, Canada
Email: harimsri@math.uvic.ca

Dr. Muhammad Arif
Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Email: marifmaths@awkum.edu.pk

Dr. Mohsan Raza
Government College University, Faisalabad 38000, Pakistan
Email: mohsanraza@gcuf.edu.pk

Manuscript Topics

The quantum (or q-) calculus is a very crucial area of study within the field of classical mathematical analysis. It focuses on a potentially useful generalization of the operations of integration and differentiation. It is a comprehensive field for research in Mathematics which has its historical roots as well as a renewed scope in the current times. It is important to note that the long history of the quantum calculus dates back to the work of Bernoulli and Euler. But, certainly, it has drawn the attention of modern mathematicians in the last several decades, which is due particularly to its extensive areas of application. It involves complex calculations and computations which make it difficult as compared to the rest of the subjects in mathematics. Now-a-days there is a rapid growth of activities in the area of the q-calculus and its applications in various fields such as mathematics, mechanics, and physics. The history of the study of the q-calculus may be illustrated by its wide variety of applications in quantum mechanics, analytic number theory, theta and mock theta functions, hypergeometric functions, theory of finite differences, gamma function theory, Bernoulli and Euler polynomials, combinatorics, multiple hypergeometric functions, Sobolev spaces, operator theory, and, more recently in the geometric theory of analytic and harmonic univalent functions.
The above-mentioned areas of application of the q-calculus have caused utmost importance to research in the q-calculus. Other than these areas, basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials, also have found vast areas of application, such as number theory and the theory of partitions. As a matter of fact, basic (or q-) hypergeometric functions are used in many diverse fields including combinatorial analysis, finite vector spaces, Lie theory, particle physics, nonlinear electric circuit theory, mechanical engineering, theory of heat conduction, quantum mechanics, cosmology and statistics.

Aims and Scope
This proposal is motivated essentially by the following recently-published survey-com-expository review article by the Lead Guest Editor (Professor Hari Mohan Srivastava) in which significant emphasis has been systematically put not only the usages of the quantum (or q-) calculus, but also of the fractional q-calculus, in Geometric Function Theory of Complex Analysis:
H. M. Srivastava, Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans. A: Sci. 44 (2020), 327-344 [DOI: https://doi.org/10.1007/s40995-019-00815-0].0123456789().,-volV)(0123456789,-().volV)
The purpose of this special issue is to further encourage researches in the q-calculus and the fractional q-calculus, especially in the context of the geometric function theory of complex analysis. We sincerely believe that it will motivate further researchers leading to some valuable contributions and further developments on these and other related topics. Our main idea to propose this special issue is primarily based upon the fact that the researches in geometric function theory of complex analysis using the classical q-calculus and the fractional q-calculus have a great potential for applications. This platform will help the active researchers to present their work and share their ideas with the interested research community.

Paper submission
All papers will be carefully refereed before publication.
Submission due date: 30 December 2020

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H. M. Srivastava, Sheza M. El-Deeb
AIMS Mathematics, 2020, 5(6): 7087-7106. doi: 10.3934/math.2020454
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