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.
Harmonic convexity is very important new class of non-convex functions, it gained prominence in the Theory of Inequalities and Applications as well as in the rest of Mathematics’s branches. The harmonic convexity of a function is the basis for many inequalities in mathematics. Furthermore, harmonic convexity provides an analytic tool to estimate several known definite integrals like \(\int_{a}^{b} \frac{e^{x}}{x^{n}}dx\), \(\int_{a}^{b} e^{x^{2}} dx\), \(\int_{a}^{b} \frac{\sin x}{x^{n}}dx\) and \(\int_{a}^{b} \frac{\cos x}{x^{n}}dx\) \(\forall n \in \mathbb{N}\), where \(a,b \in (0,\infty)\). In this article, some un-weighted inequalities of Hermite-Hadamard type for harmonic log-convex functions defined on real intervals are given.
Mathematical modeling of infectious diseases has progressed dramatically over the past four decades and continues to flourish at the nexus of mathematics, epidemiology, and infectious diseases research. Now recognized as a valuable tool, mathematical models are being integrated into the public health decision-making process more than ever before. In this article, a mathematical model of Ebola virus which is named as SEIVR (susceptible, exposed, infected, vaccinated, recovered) model is considered. First, we formulate the model and present the basic properties of the proposed model. Then, basic reproductive number is obtained by using the next-generation matrix approach. Furthermore, the sensitivity analysis of \(R_0\) is also discussed, all the endemic equilibrium points related to the disease are derived, a condition to investigate all possible equilibria of the model in terms of the basic reproduction number is obtained. In last, numerical simulation is presented with and without vaccination or control for the proposed model.
In literature, there are many methods for solving nonlinear partial differential equations. In this paper, we develop a new method by combining Adomian decomposition method and Shehu transform method for solving nonlinear partial differential equations. This method can be named as Shehu transform decomposition method (STDM). Some examples are solved to show that the STDM is easy to apply.
In this paper, we study the generalized porous medium equations with Laplacian and abstract pressure term. By using the Fourier localization argument and the Littlewood-Paley theory, we get global well-posedness results of this equation for small initial data \(u_{0}\) belonging to the critical Fourier-Besov-Morrey spaces. In addition, we also give the Gevrey class regularity of the solution.
In this paper, we study the dynamical behavior of solutions for the stochastic strongly damped wave equation with linear memory and multiplicative noise defined on \(\mathbb{R}^{n}\). Firstly, we prove the existence and uniqueness of the mild solution of certain initial value for the above-mentioned equations. Secondly, we obtain the bounded absorbing set. Lastly, We investigate the existence of a random attractor for the random dynamical system associated with the equation by using tail estimates and the decomposition technique of solutions.
With the establishment of 200-mile territorial zone in the Bay of Bengal for most countries having coastlines. The control of fishing in these zones has become highly regulated by these countries concerned. In this sense, fishing in territorial waters can be considered a sole owner fishery problem. If the people of a country are allowed to fish freely in the territorial zones, it can be termed as an open access fishery. In an open access fishery, the exploitation of fishing opportunity is completely uncontrolled. This study deals with the problem of harvesting in the prey-predator fishery model in the open access zones and seeks a plan for prey for sustainable fishing, particularly in Sundarbans ecosystem which is situated in the coastal area of the Bay of Bengal. The positive steady state of both local and global stability has been established. Optimal harvesting strategy is also studied for these purposes.
In this article, we introduce new subclasses of normalized analytic functions in the unit disk \(U\), defined by a generalized Raducanu-Orhan differential Operator. Various results are driven including coefficient inequalities, growth and distortion theorem, closure property, \(\delta$\)-neighborhoods, extreme points, radii of close-to-convexity, starlikeness and convexity for these subclasses.
