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In this paper, the Hydon method to determine discrete symmetries for a differential equation is employed to construct discrete symmetries for a family of ordinary, partial, and fractional differential equations. An application of those discrete symmetries to construct other solutions from known ones is illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a fractional order into a psoriasis model. The system is composed of two fractional equations; we prove the local existence and uniqueness of the solution of the fractional psoriasis system; some stability conditions of the model equilibrium are given; finally, we further present some numerical results that confirm the stability. [ABSTRACT FROM AUTHOR]

In this paper, the Lie symmetry algebra admitted by the time fractional Black–Scholes equation is obtained by using the Lie group method. The constructed symmetry generators are investigated to construct a family of exact solutions and conservation laws for the studied equation. At the same time, the family of solutions is extended by using the invariant subspace method. [ABSTRACT FROM AUTHOR]

The emergence of Unified Modeling Language (UML) as a standard for modeling systems has encouraged the use of automated software tools that facilitate the development process from analysis through coding. The UML state machine diagram is used for modeling the dynamic aspects of systems and includes many concepts that are not present in most popular programming languages, like Java or C++. There exists a gap between high level modeling language and a programming language. This paper proposes an approach to narrow the gap between multiple UML models and an implemented system. The narrowing of gap is achieved by generating compact and efficient Java code directly from UML state machine having sequential and concurrent substates. The code generation is achieved by creating a mapping between UML behavior and the Java programming language. Our model can work as a basis for automatic code generation for object-oriented systems. [ABSTRACT FROM AUTHOR]

Using a fixed point theorem in a Banach algebra, we prove an existence result for a fractional functional differential equation in the Riemann-Liouville sense. Dependence of solutions with respect to initial data and an uniqueness result are also obtained. [ABSTRACT FROM AUTHOR]

We investigate a system of two coupled harmonic oscillators on the noncommutative plane ${\mathbb R}^2_\theta$ by requiring that the spatial coordinates do not commute. We show that the system can be diagonalized by a suitable transformation, i.e. a rotation with a mixing angle α. The obtained eigenstates as well as the eigenvalues depend on the noncommutativity parameter θ. Focusing on the ground state wave function before the transformation, we calculate the density matrix ρ0(θ) and find that its traces Tr(ρ0(θ)) and ${\rm Tr}(\rho_0^2(\theta))$ are not affected by the noncommutativity. Evaluating the Wigner function on ${\mathbb R}^2_\theta$ confirms this. The uncertainty relation is explicitly determined and found to depend on θ. For small values of θ, the relation is shifted by a θ2 term, which can be interpreted as a noncommutativity correction. The calculated entropy does not change with respect to the normal case. We consider the limits α = 0 and α = π/2. In the first case, by identifying θ to the squared magnetic length, one can recover basic features of the Hall system. [ABSTRACT FROM AUTHOR]