Abstract and Applied Analysis

In this paper, we extend the results obtained by Ezearn on annihilated points for his higher-order nonexpansive mappings to the context of general higher-order nonexpansive mappings. Precisely in his thesis, Ezearn introduced the concept of annihilated points, which extends the notion of fixed points, and it is only meaningful in the context of higher-order nonexpansive mappings and gave some mild conditions when the annihilated points could exist in strictly convex Banach spaces. In the last direction, we also extend Ezearn’s result on the approximate fixed point sequence for higher-order nonexpansive mappings to general higher-order nonexpansive mappings.

Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing the extended Pochhammer matrix symbol. First, we present the extended hypergeometric matrix function and express certain integral equations and differential formulae concerning it. We also present the Mellin matrix transform of the extended Wright hypergeometric matrix function. After that, we present some fractional calculus findings for these expanded Wright hypergeometric matrix functions. Lastly, we present several theorems of the extended Wright hypergeometric matrix function in fractional Kinetic equations.

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter and singular in a complex time variable at the origin. These equations combine differential operators of Fuchsian type in time and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the parameter known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic-type functions in time and are bounded holomorphic in space. A set of logarithmic-type solutions are shaped by means of Laplace transforms relatively to and and Fourier integrals in space. Furthermore, a formal logarithmic-type solution is modeled which represents the common asymptotic expansion of the Gevrey type of the genuine solutions with respect to on bounded sectors at the origin.

The COVID-19 (coronavirus disease) pandemic represents a global public health emergency unprecedented in recent history. This explains the growing interest of scientists in this subject. Indeed, the question of the COVID-19 pandemic has led to numerous scientific works, with the aim of estimating the reproduction number, the start date of the epidemic or the cumulative incidence. Their results have contributed to epidemiological surveillance and informed public health policy decisions. In our work, using basic data and statistics from the city of Ouagadougou in Burkina Faso, we first consider a mathematical model of COVID-19 transmission taking into account the possibility of transmission from dead populations to susceptible populations; then, we use another method which is the sentinel’s method of JL Lions to estimate the number of infected populations without any time trying to know the beginning of the epidemic; finally, we highlight the numerical simulation of the considered model solution.

Lipschitz in the small is a generalization of the Lipschitz condition. The Lipschitz condition guarantees the uniqueness of the solution of the initial value problems. A special Lipschitz condition in the small is a contraction in the small. Based on the Lipschitz in the small in this paper, fixed-point theorems involving contraction in the small will be presented. The results will be applied to develop Picard’s theorem.

In this article, a singularly perturbed convection-diffusion problem with a small time lag is examined. Because of the appearance of a small perturbation parameter, a boundary layer is observed in the solution of the problem. A hybrid scheme has been constructed, which is a combination of the cubic spline method in the boundary layer region and the midpoint upwind scheme in the outer layer region on a piecewise Shishkin mesh in the spatial direction. For the discretization of the time derivative, the Crank-Nicolson method is used. Error analysis of the proposed method has been performed. We found that the proposed scheme is second-order convergent. Numerical examples are given, and the numerical results are in agreement with the theoretical results. Comparisons are made, and the results of the proposed scheme give more accurate solutions and a higher rate of convergence as compared to some previous findings available in the literature.