In this article, a mathematical model of the COVID-19 pandemic with control parameters is introduced. The main objective study to determine most effective for predicting transmission dynamic using deterministic variables. For purpose, we introduce three variables reduce number infected and asymptomatic or undiagnosed populations in considered model. Existence necessary optimal conditions are al...

‎in this paper‎, ‎we introduce fractional-order into a model of hiv-1 infection of cd4^+ t--cells‎. ‎we study the effect of ‎the changing the average number of viral particles $n$ with different sets of initial conditions on the dynamics of‎ ‎the presented model‎. ‎ ‎the nonstandard finite difference (nsfd) scheme is implemented‎ ‎to study the dynamic behaviors in the fractional--order hiv-1‎‎i...

This paper is a review of the authors’ results on the Dynamical Systems Method (DSM) for solving operator equation (*) F (u)= f . It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F . It is assumed that F is continuously Fréchet differentiable, but no smoothness assumptions on F ′(u) are imposed. The DSM for solving equation (*) ...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

We prove in the general setting of lower semicontinuous functions on Banach spaces the relation between the Rockafellar directional derivative and the mixed lower limit of the lower Dini derivatives. As a byproduct we derive the famous inclusions of tangent cones of closed sets in Banach spaces. The results are established using as principal tool multidirectional mean value inequalities [Aussel...

We define the notions of unilateral metric derivatives and “metric derived numbers” in analogy with Dini derivatives (also referred to as “derived numbers”) and establish their basic properties. We also prove that the set of points where a path with values in a metric space with continuous metric derivative is not “metrically differentiable” (in a certain strong sense) is σsymmetrically porous ...

Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method ...

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

We complete the study of Manin triples of real simple Lie algebras. In the Part 2 of the article we classify the Manin triples (g(R), W, g(R) ⊕ g(R)) (case 2 of the doubles) up to weak and gauge equivalence. First we recall the main definitions of the Part 1. Definition 1. Let g 1 , g 2 , d be Lie algebras over a field K and let Q be a symmetric nondegenerate bilinear form on d. A triple (g 1 ,...

a green and efficient one-pot, four-component synthesis of 6-amino-4-aryl-3-methyl-2,4-dihydropyrano[2,3- c ]pyrazo-carbonitrile derivatives catalyzed by borax in water is described. this method provides several advantages such as environmental friendliness, shorter reaction time, excellent yields, and simple workup procedure. the in vitro cytotoxic activity of the synthesized test compounds wa...