Modeling Language (UML) has become a de facto standard for design,
specification and modeling of object oriented software systems. UML structures
being graphical in nature lack defining semantics of the systems and are prone
to causing errors. Formal methods are proved to be a powerful tool for
requirement analysis, design and specification of software systems. Hence,
linking UML with formal approaches will
enhance modeling power of software systems. In this paper, an approach is
developed by integrating UML and Z notation focusing on equivalence relation of
the state diagrams. The Z is used because it is based on the first order predicate logic having rigorous computer tool support. The
reflexivity, symmetry and transitivity properties, being important at design
level, are identified and described. It is believed that this approach will be
effective and useful at both academics and industrial level. The need,
reasoning and benefits of the integrated approach are discussed. The resultant
formal models are analyzed and validated using Z/Eves tool.
In this article, a new application to find the exact solutions of nonlinear partial time-space fractional differential Equation has been discussed. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential Equations into nonlinear ordinary differential Equations. Afterwards, the (G'/G)-expansion method has been implemented, to celebrate the exact solutions of these Equations, in the sense of modified Riemann-Liouville derivative. As application, the exact solutions of time-space fractional Burgers’ Equation have been discussed.