Ahmed M. Kareem

University of Diyala · College of Science , Mathematics department

In this paper, the deterministic and the stochastic models are proposed to study the interaction of the Coronavirus (COVID-19) with host cells inside the human body. In the deterministic model, the value of the basic reproduction number R0 determines the persistence or extinction of the COVID-19. If R0 < 1, one infected cell will transmit the virus...

In this paper, we model the spread of coronavirus (COVID -19) by introducing stochasticity into the deterministic differential equation susceptible -infected-recovered (SIR model). The stochastic SIR dynamics are expressed using Itô's formula. We then prove that this stochastic SIR has a unique global positive solution I(t).The main aim of this art...

Abstract:This paper introduce two different definitions of fractional derivatives, namely Riemann-Liouville and Caputo derivatives , and some basics properties of these derivatives are discussed, conformable fractional derivative are addressed .The paper focuses on the conditions needed in order to guarantee the general solution when we have the pa...

In this article, we analyze stochastic differential equations model for internal Coronavirus (COVID-19) dynamics. The stochastic differential equations model are expressed using the Ito's formula. The Environmental Stochasticity in this dynamical model is presented via parameters disturbance which is the standard method in the stochastic differenti...

In this paper, we suggest a new method for solving fractional initial value problems of different fractional orders. We call it hybrid Series Solution (Fractional with power, Fractional with fractional, Fractional with power and fractional). The main difference between Caputo and Riemann-Liouville formulas for the fractional derivatives as mentione...

In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed. The difference between Caputo and Riemann – Liouville formulas for the fractional derivatives also ment...

In this thesis, I pointed out three very recent applications of the new established fractional Caputo-Fabrizio derivative and I discussed its related properties and theorems. The associated fractional integral was displayed and the Laplace transform of the Riemann-Liouville and Caputo fractional differential operators was presented.