Special Session 1

Computational and Transform Methods Applications to Differential Equations and Systems

  • Fethi B. M. Belgacem, Kuwait
  • Carlo Cattani, Italy
  • Amar Debbouche, Algeria

Participants of the ICMCMST'15 are invited to submit articles that include- but are not limited to- the scope indicated by the session title, concerning wide range applications as well as theoretical investigations of single or systems of differential equations, be they typical or functional, ordinary or partial, continuum- related or stochastic, of integer order or fractional  type.  Investigative tools may include transform theory techniques, or any well known or new numerical, variational, or statistical methods. Related engineering applications, applied and theoretical physics investigations, statistical studies, educational research cases, as well as economico-financial mathematics type manuscripts will be most welcome.

Special Session 2

Fuzzy Differential Equations: Theory and Applications

  • Dumitru Baleanu, Romania
  • Alireza Khastan, Iran
  • Juan J. Nieto, Spain

Fuzzy differential equations (FDEs) appears as a natural way to model the uncertainty in dynamical environments. When a real world problem is transformed into a deterministic ordinary differential equation, or a system of differential equations, we cannot usually be sure that the model is perfect. For example, the initial values may not be known exactly and the functions may contain uncertain parameters. Therefore it is natural to consider differential equations in the fuzzy concept. For the initiation of this aspect of fuzzy theory, the necessary calculus of fuzzy functions such as fuzzy derivatives and fuzzy integrals has also been studied. Consequently the study of the theory of FDEs has recently been growing rapidly as an independent discipline. In the recent years, the concept of Fuzzy Initial Value Problems (FIVPs), Fuzzy Partial Differential Equations (FPDEs) and Fuzzy Fractional Differential Equations (FFDEs) has been proposed. Some new approaches and new derivatives are introduced to study the new properties of FDEs. It is therefore appropriate to gather current trends and provide a high quality forum for the theoretical research results and practical development of FDEs.

Objectives and topics:

The aim of this special session is to present recent developments in the theory and applications of the fuzzy differential equations.

The topics include but are not limited to:

  • Theoretical aspects of fuzzy differential equations,
  • Numerical methods to solve FDEs, FFDEs and FPDEs,
  • Relation between FDEs and Interval Differential Equations (IDEs),
  • Fuzzy derivatives and integrals and its application to FDEs,
  • Applications of FDEs in the real world problems.

Special Session 3

Trends on Fractional Operators and Their Applications

  • Abdon Atangana, South Africa
  • Dumitru Baleanu, Romania
  • Hossein Jafari, Iran

Fractional calculus has gained interest in many branches of sciences and engineering due to its capability to describe accurately the dynamics of the real world problems.  Despite of the fact that the researchers have produced many good results, there are still many opened problems within this field and also untouched branches of sciences in which the concept of fractional calculus has not been applied yet. The aim of this special section is to gather together researchers working in this field and collect new findings from their recent research activities.

Objectives and topics:

The aim of this special session is to present recent developments in the theory, methods and applications of fractional calculus.

The topics include but are not limited to:

  • Analytical methods for fractional differential equations,
  • Numerical methods for fractional differential equations,
  • Theory on new definitions of derivatives with fractional order,
  • Iterative methods for nonlinear fractional differential equations,
  • Modeling with fractional derivative,
  • Existence and uniqueness theory of fractional differential equations.