Local existence and uniqueness for a fractional SIRS model with Mittag–Leffler law

In this paper, we study an epidemic model with Atangana-Baleanu-Caputo fractional derivative. We obtain a special solution using an iterative scheme via Laplace transformation. Uniqueness and existence of a solution using the Banach fixed point theorem are studied. A detailed analysis of the stability of the special solution is presented. Finally, our generalized model in the derivative sense is solved numerically by the Adams-Bashforth-Moulton method.

Rotational λ – hypersurfaces in Euclidean spaces

Self-similar flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, \lambda -hypersurfaces are the generalization of self-similar hypersurfaces. In the present article we consider \lambda -hypersurfaces in Euclidean spaces which are the generalization of self-shrinkers. We obtained some results related with rotational hypersurfaces in Euclidean 4-space \mathbb{R}^{4} to become self-shrinkers. Furthermore, we classify the general rotational \lambda -hypersurfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational \lambda -hypersurfaces in \mathbb{R}^{4}.

Wave Optics in the Kerr Space-Time Taking the Spin-Helicity Interaction into Account

We apply an algebraically special solution of the Maxwell equations in the Kerr space-time, which we specify as outgoing in the Chandrasekhar meaning, to obtain the wave vectors of right- and left-polarized waves and prove that the nullity condition of field invariants yield the non-nullity of wave vectors and that the wave vector is not geodesic. We also show how these are related to the analysis of radiation in the Kerr space-time, provided by Starobinskii and Teukolsky.

Comparative Study of Wellhole Surrounding Rock under Nonuniform Ground Stress

The stress analysis of the wellhole surrounding rock and the regular failure of the wellhole has always been a concern for the well builders. Firstly, the Hamilton canonical equations are obtained by using the Hamiltonian variational principle in the sector domain, and the zero eigensolution and nonzero eigensolutions of the homogeneous equation are solved. According to the Hamiltonian operator matrix with the orthogonal eigenfunction system, the special solution form of the nonhomogeneous boundary condition equation is obtained. Then, according to the principle of the same coefficient being equal, the relationship equation between the direction eigenvalue and the angle coefficient is obtained, from which the specific expression of the special solution of the equation can be determined. Furthermore, the analytical solution of the wellhole surrounding rock problem under nonuniform ground stress is obtained by using the linear elastic accumulative principle. Finally, a concrete example is given to compare the finite element method and the symplectic algorithm. The results are consistent, which ensures the accuracy and the reliability of the symplectic algorithm. The relationship between the circumferential stress distribution around the hole and the lateral pressure coefficient is further analyzed.

Geometric description of a discrete power function associated with the sixth Painlevé equation

In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with W ~ ( 3 A 1 ( 1 ) ) symmetry. By constructing the action of W ~ ( 3 A 1 ( 1 ) ) as a subgroup of W ~ ( D 4 ( 1 ) ) , i.e. the symmetry group of P VI , we show how to relate W ~ ( D 4 ( 1 ) ) to the symmetry group of the lattice. Moreover, by using translations in W ~ ( 3 A 1 ( 1 ) ) , we explain the odd–even structure appearing in previously known explicit formulae in terms of the τ function.