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# Open Engineering: Recent Trends in Mathematical Analysis and their Applications

### DESCRIPTION

Many times during the solution of complex problems in engineering, we treat with important functions defined by improper integrals and series (or infinite products). Those functions are generally called special functions. Special functions contain a very old branch of mathematics. For example, trigonometric functions have been studied for over a thousand years, due mainly to their numerous applications in astronomy. Yet the origins of their unified and rather complete theory date back to the nineteenth century. From application points of view, special functions as important mathematical tools rest on, due to their remarkable properties, usefulness for the applied scientists and engineers, as Paul Turan once remarked that special functions would be more appropriately labeled useful functions. Various special functions like Bessel and all cylindrical functions; the Gauss, Kummer, confluent and generalized hypergeometric functions; the classical orthogonal polynomials, the incomplete Gamma and Beta functions and error functions, the Airy, Whittaker functions and so on, will provide solutions to integer order differential equations and systems, used as mathematical models. However, recently there has been an increasing interest in and widely extended use of differential equations and systems of fractional order (that is, of arbitrary order), as better models of phenomena of various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus (branch of Mathematical Analysis) are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations.

This issue provides learners with the opportunity to develop an understanding of special functions and the skills needed to apply advanced mathematical techniques to solve complex engineering problems. Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this special issue is to highlight the importance of fundamental results and techniques of the theory of mathematical analysis, and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.

Specific topics include but are not limited to

• Sequence and series in functional analysis
• Special functions related to fractional (non-integer) order control systems and equations
• Various special functions related to generalized fractional calculus
• Operational method in fractional calculus
• Functional analysis and fractional operators
• Mathematical techniques and applications in fractional optimizations, biology and physics
• Applications of numerical analysis and applied mathematics
• Computational mathematics involving special functions
• Fractional techniques in mathematical modeling

We seek high-quality original research papers, as well as communications and survey papers related to the topic of this issue.

Tentative Submission Schedule
Manuscript submission due: November, 2017
First round of reviews: February, 2018

Publication date: May, 2018

### EDITED BY

Lead Guest Editor:
Praveen Agarwal, Department of Mathematics, Anand International College of Engineering, India
E-mail: goyal.praveen2011@gmail.com

Guest Editors:
Taekyun Kim, Department of Mathematics, Kwangwoon University, Seoul, 139-701, Republic of Korea
E-mail:tkkim@kw.ac.kr
Adem Kilicman, Department of Mathematics, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia
E-mail:akilic@upm.edu.my

### HOW TO SUBMIT

Before submission authors should carefully read the Instructions for Authors, which are located here. All submissions to the Special Issue must be made electronically at via online submission system Editorial Manager.
All manuscripts will go through the Open Engineering high standards, quick, fair and comprehensive peer-review procedure.
When entering your submission via online submission system please choose the type article Topical Issue Recent Trends in Mathematical Analysis and their Applications
The deadline for the submissions is 30.10.2017, but individual papers will be reviewed and published online as they arrive.

Contributors to the Special Issue will benefit from:

• fair and constructive peer review provided by recognized experts in the field,
• Open Access to your article for all interested readers,
• fast online publication of articles,
• online submission and tracking system,
• free language assistance for authors from non-English speaking regions;
• increased visibility and readership
• increased and accelerated citations
• no space constraints
• extensive promotion of best articles

We are looking forward to your submission. If you have any question, please contact us:

Managing Editor: Karolina.Hejbudzka@degruyteropen.com