Journal of Advances in Applied Mathematics

7

Authors: Yu Wang, Yong Yu

The aim of this paper is to study two particular GV-semigroups whose full subsemigroups form 0-semidistributive lattices. The structure of GV-inverse semigroups whose full subsemigroup lattices are 0-semidistributive is first characterized. Moreover, much more explicit structural description is obtained for orthodox GV-semigroups by establishing an inverse semigroup congruence.

10

Authors: Ruiying Wang, Shouqiang Du, Zhimin Liu

In this paper, we consider the Newton type methods for solving the nonsmooth equations with finitely many maximum functions. A new ∂∗-differential is used in the given Newton-type methods. The Newton-type methods also include a new parameterized combination. The superlinear convergence of the given methods is presented. Finally, the numerical experiments highlight the efficiency of the given methods.

11

Authors: Amine Bernoussi, Abdelilah Kaddar, Said Asserda

In this paper, we investigate the global asymptotic stability of the possible equilibria for an SIRI epidemic model with a distributed latent period and a general incidence function. By using the method of Lyapunov functions and the LaSalle invariance principle, we show that the global asymptotic stability is completely determined by the basic reproduction number R0. The originality of this work is to have a basic reproduction number R0 which depends on the distribution of the latent period. Finally, we use a nonstandard discretization method of Mickens to illustrate numerically our theoretical results.

19

Authors: Bhuvaneswari Sambandham, Aghalaya S Vatsala

Generalized monotone method together with coupled lower and upper solutions yield monotone sequences which converge uniformly and monotonically to coupled minimal and maximal solutions of the nonlinear problem under consideration. In this work, we have developed generalized monotone method for sequential Caputo fractional boundary value problem with mixed boundary conditions which are in terms of Caputo fractional derivative. For that purpose, we have obtained a representation form for the corresponding linear Caputo sequential boundary value problem in terms of the Green’s function. In addition, we have obtained a linear comparison result for the linear sequential differential inequalities with linear mixed boundary conditions. The comparison result is useful in proving the monotonicity of the iterates as well as the uniqueness of the solution of the nonlinear sequential boundary value problem. Our method yields the integer results as a special case. Some numerical examples for the linear sequential Caputo fractional boundary value problems have also been presented.