The need for Interdisciplinary research is being felt strongly and with this aim in mind we would like to purpose this Special Issue which aims to publish original high quality research or survey articles on recent research in areas of pure and applied mathematics. We would like to invite papers not only on theoretical and conceptual works but also application of mathematics in various fields. Such a broad spectrum is considered to provide a platform to academicians and researchers of the world to bring forth the latest advancements in mathematical techniques applicable to several branches of mathematics, physics, chemistry, biology, engineering and all applied sciences.

The aim of this special issue is to explore new research techniques to study complex biological systems by mathematical, optimization and statistical methods. Coverage of applications includes any branch of science and technology such as fluid mechanics, mathematical biology, control theory, and inverse problems.

It is predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.

Computational and applied mathematics covers area of control theory, game theory, networks, optimization, computational sciences, information technology, mechatronics, and economic and energy systems. Original research results in these and related areas, that use state-of-art mathematical tools, find in this journal, a natural home, and an outlet to the broader scientific community.

Fractional Calculus gained great interest in the researchers' community due to its wide applications in several branches of Applied Mathematics and Sciences.

Due to the nonlocal nature of fractional derivative, many dynamical systems can be described in a more precise way by using fractional order differential equations. Hence in many cases such equations appear as important alternatives for integer order differential equations. Various natural systems in the fields such as viscoelasticity, electrical circuits and nonlinear oscillations of earthquake show an intermediate behavior which can only be modeled using fractional order differential equations.

The purpose of this special issue on “Analysis and applications of fractional calculus” is to invite the papers that deal with the theory, qualitative analysis, numerical techniques and applications of various kinds of fractional differential equations, fractional integral equations, fractional integro-differential equations and fractional partial differential equations.

During the past few decades, fractional calculus found many applications in various fields of physical sciences such as viscoelasticity, diffusion, control, relaxation processes, biology, physics and engineering, and other applications. The main interest of this special issue is in papers that describe and analyze new applicable techniques for solving scientific or engineering problems. Original papers dealing with new methods such as modified decomposition methods, homotopy methods, and variational methods and like these for finding analytical or semi-analytical solutions are sought. In this special issue, we invite original research articles as well as review articles describing the recent advances in fractional modeling.

Nonlinear Differential Equation have been widely used in many areas of physics and engineering and are of significant importance in mechanical and structural dynamics for the comprehensive understanding and accurate prediction of motion and deformation. The problems facing engineers, physicists and applied mathematicians today exhibit certain essential features which preclude exact analytical solutions. Some of these features are nonlinearities, variable coefficients, complex boundary shapes, and nonlinear boundary conditions at known or, in some cases, unknown boundaries. The study of such equations is of interest to many researchers and various methods of solution have been proposed. The solution of governing equations due to limitation of existing exact solutions have been one of the most time-consuming and difficult affairs among researchers of nonlinear problems. The purpose of this issue is to get acquainted with methods dealing with nonlinearities.

The aim of this special issue is to explore new research techniques to study complex biological systems by mathematical, optimization and statistical methods. Coverage of applications includes any branch of science and technology such as fluid mechanics, mathematical biology, control theory, and inverse problems.

It is predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.

The purpose of the special issue on Advances in Applied and Structural Mechanics is to explore the latest advances on modeling, computational analysis and numerical simulation. It offers a concentrative venue for researchers to make rapid exchange of ideas and original research findings in Applied and Structural Mechanics.

Fuzzy sets were introduced by L. A. Zadeh on 1965 as an extension of the classical notion of set. This theory has articulated systematically and rigorously the intuition that there is so diffuse as to the degree of belonging to classes (that is, to possess certain properties) and that with respect to certain classes, membership degrees are infinite. Now, there are many mathematical constructions similar to or more general than fuzzy sets.

Since fuzzy sets were introduced in 1965, a lot of new mathematical constructions and theories treating imprecision, inexactness, ambiguity, and uncertainty have been developed. Some of these constructions and theories are extensions of fuzzy set theory, while others try to mathematically model imprecision and uncertainty in a different way (for example: interval sets, L-fuzzy sets, set-valued sets, interval-valued fuzzy sets, intuitionistic L-fuzzy sets, neutrosophic sets, soft sets, ..).

The enormous fertility of fuzzy sets theory has been shown to load capable of new and suggestive scientific approaches in various fields, from medicine to linguistics and economics, not forgetting, of course, the various branches of mathematics and technology.

All areas related with fuzzy sets theory are welcome for this special issue.

The special issue on recent advances in Applied and computational Mathematics addresses work at the interface between applied mathematics, numerical computation and appplications of systems oriented ideas to the physical, biological, social and behavioral sciences and emphasizes papers of a computational nature focussing on new algorithms, their analysis and numerical results.

Nonlinear systems have been widely used in many areas of physics and engineering and are of significant importance in mechanical and structural dynamics for the comprehensive understanding and accurate prediction of motion and deformation. The study of nonlinear systems is of interest to many researchers and various methods of solution have been proposed. Surveys of the literature with numerous references, and useful bibliographies, have been given by Nayfeh, Mickens, Jordan and Smith and more recently by He.

Solving of governing equations due to limitation of existing exact solutions have been one of the most time-consuming and difficult affairs among researchers of nonlinear problems. With the rapid development of nonlinear science, there appears an ever-increasing interest of scientists in the analytical asymptotic techniques for nonlinear Problems and several analytical approximate methods have been developed to solve linear and nonlinear ordinary and partial differential equations.