Open Journal of Mathematical Analysis (OMA)

In this paper, we develop a mathematical deterministic modeling approach to model measles disease by using the data pertinent to Nigeria. Control measure was introduced into the susceptible and exposed classes to study the prevalence and control of the measles disease. We established the existence and uniqueness of the solution to the model. From the simulation results, it was realized that the control introduced on the susceptible class; and exposed individuals at latent period play a significant role in controlling the disease. Furthermore, it is recognized that if more people in the susceptible class get immunization and the exposed people at the latent period goes for treatment and therapy during this state before they become infective, the disease will be eradicated more quickly with time.

This work deals with a coupled system of wave with past history effective just in one of the equations. We show that the dissipation given by the memory effect is not strong enough to produce exponential decay. On the other hand, we show that the solution of this system decays polynomially with rate \(t^{-\frac{1}{2}}\). Moreover by recent result due to A. Borichev and Y. Tomilov, we show that the rate is optimal. To the best of our knowledge, there is no result for optimal rate of polynomial decay for coupled wave systems with memory in the previous literature.

In this article, we give new conditions on the fast growing analytic coefficients of linear complex differential equations to estimate the iterated \(p\)-order and iterated \(p\)-type of all solutions in the unit disc \(\mathbb{D}\), where \(p\in \mathbb{N}\backslash \{1\}\).

This work handle a mathematical model describing the process of contact between a piezoelectric body and rigid foundation. The behavior of the material is modeled with a electro-elastic constitutive law. The contact is formulated by Signorini conditions and Coulomb friction. A new decoupled mixed variational formulation is stated. Existence and uniqueness of the solution are proved using elements of the saddle point theory and a fixed point technique. To show the efficiency of our approach, we present a decomposition iterative method and its convergence is proved and some numerical tests are presented.

In this paper, we consider a neutral mixed type difference equation, and obtain explicitly sufficient conditions for asymptotic behavior of solutions. A necessary condition is provided as well. An example is given to illustrate our main results.

The equation \(v=v_0+\int_0^t(t-s)^{\lambda -1}v(s)ds\) is considered, \(\lambda\neq 0,-1,-2…\) and \(v_0\) is a smooth function rapidly decaying with all its derivatives. It is proved that the solution to this equation does exist, is unique and is smoother than the singular function \(t^{-\frac 5 4}\).

The aim of this paper is to construct left sided and right sided integral operators in a unified form. These integral operators produce various well known integral operators in the theory of fractional calculus. Formulated integral operators of this study include generalized fractional integral operators of Riemann-Liouville type and operators containing Mittag-Leffler functions in their kernels. Also boundedness of all these fractional integral operators is derived from the boundedness of unified integral operators. The existence of new integral operators may have useful consequences in applied sciences besides in fractional calculus.

In this paper, we explore the existence of nontrivial solution for the fifth-order three-point boundary value problem of the form \(u^{(5)}(t)+f(t,u(t))=0,\quad\text 0<t<1,\) with boundary conditions \(u(0)=0,\quad u^{‘}(0)=u^{”}(0)=u^{”’}(0)=0,\quad u(1)=\alpha u(\eta),\) where \(0<\eta<1\), \(\alpha\in\mathbb{R}\), \(\alpha\eta^{4}\neq1\), \(f\in C([0,1]\times\mathbb{R},\mathbb{R})\). Under certain growth conditions on the non-linearity \(f\) and using Leray-Schauder nonlinear alternative, we prove the existence of at least one solution of the posed problem. Furthermore, the obtained results are further illustrated by mean of some examples.

Polynomiography is the art and science of visualization in approximation of zeros of polynomials. In this report, we visualize polynomiography of some complex polynomials via iterative methods presented in [1].

In this paper, we use the Banach fixed point theorem to obtain the existence, interval of existence and uniqueness of solutions for nonlinear hybrid implicit Caputo-Hadamard fractional differential equations. We also use the generalization of Gronwall’s inequality to show the estimate of the solutions.