Special Sessions

Special Session 1

New trends in fractional order systems: Theory & Applications


  • Konrad A. Markowski, Poland
  • Carla M.A. Pinto, Portugal

Fractional Calculus is an old research topic, with more than 300 years of dedicated research. The idea of fractional calculus has been known since the classical "integer" calculus, with the first reference probably being associated with Leibniz and L'Hospital in 1695. It is regarded as a branch of mathematical analysis dealing with integro-differential equations in which the integrals are of the convolution type and weakly singular kernels of the power-law type. This special session is a place for researchers and practitioners sharing ideas on the theories, applications, numerical methods and simulations of fractional calculus and fractional differential equations.

The main topics of interest are enumerated in the below and submissions in the relevant fields are welcome:

  • Numerical and analytical fractional order systems,
  • Simulations for fractional models,
  • Implementation methods,
  • Approximation methods,
  • Analysis of fractional order systems,
  • Analysis, modelling and control of phenomena in: electrical engineering; mechanics; automatic control; biology; biophysics; physics.

Special Session 2

New applications of reproducing kernel Hilbert space method (RKHSM), group preserving scheme (GPS) and lie symmetry methods


  • Ali Akgul, Turkey
  • Esra Karatas, Turkey

The main focus of this session will be on the analytical, analytical approximate and numerical methods for the solution of the problems related to the applications in Engineering. This session covers many subjects: from new numerical methods and fundamental research until engineering implementations.

The organizers aim to provide a place where investigators, scientists, engineers and practitioners throughout the world can present and discuss the latest achievements and future challenges that will improve future understanding of our reality.

We invite researchers to submit their original research articles that will enhance the applications of proposed analyses approaches.

Potential topics include, but are not limited to:

  • Reproducing Kernel Method,
  • Linear, Non Linear ODEs, PDEs and FDEs,
  • Integral Equations,
  • Boundary Value Problems,
  • Applied mathematics,
  • Material Science and engineering,
  • Computational Methods,
  • Fluid-structure interactions,
  • Fractional Calculus,
  • Group Preserving Scheme,
  • Lie Symmetry.

Special Session 3

Integro-differential operators and equations, boundary value problems and numerical analysis


  • Vladimir B. Vasilyev, Russia

As a rule every mathematical model includes some differential or integral or difference equation, and mathematicians, physicists, engineers and others take part for studying such equations by different methods. First one needs to study such equations from mathematical point of view including Fredholm properties, existence and uniqueness questions in different functional spaces in which operators from these equations are acting. Then if a solution exists one needs to find this solution at least numerically, and this step requires computational and numerical solving methods. All these aspects are closely related and use often similar methods such as integral transforms, a priori estimates, fix point theorems, factorization technique, asymptotical expansion etc.

The aim of this special session is to bring together experts in these fields and to present latest studies in all aspects from the field.

Main topics include but are not limited to:

  • Differential and integral operators and equations,
  • Boundary value problems in a complex plane and multidimensional spaces,
  • Difference and discrete equations and related boundary value problems,
  • Applications of differential and integral equations to problems of mathematical physics and modeling,
  • Computational and numerical analysis for solving boundary value problems.

Special Session 4

Mathematical foundations of uncertainty modelling in applied sciences


  • Dumitru Baleanu, Romania
  • Alireza Khastan, Iran
  • Irina Perfilieva, Czech Republic

Nowadays modeling of uncertainty is present in various fields, from applications in the industry passing through applications in natural phenomena. What applied areas have in common is the presence of vague and uncertain information and the modeling done by the human being, whose reasoning is imprecise. Since mathematical tools are used to modeling all these applications, its theoretical aspects have to admit the concept of “fuzziness”.

This special session is conceived to be a forum for the exchange of ideas between researchers who are interested in mathematical foundations of uncertainty modeling and researchers who use the theory of fuzzy sets and systems in real world applications. It is therefore appropriate to gather current trends and provide a high quality forum for the theoretical research results and practical development on theory of uncertainty modeling and fuzzy sets and systems.

Objectives and topics: The aim of this special session is to present recent developments in the theory and applications of uncertainty modeling and fuzzy sets and systems.

The topics include but are not limited to:

  • Theoretical aspects of fuzzy sets and systems,
  • Fuzzy approximations, fuzzy arithmetic and Fuzzy data analysis,
  • Fuzzy Transforms and its applications,
  • Uncertainty Modeling in applied sciences,
  • Differential and integral equations with uncertainty,
  • Applications of fuzzy mathematics in the real world problems.