Mathematics - Publication
2 Publications found
Caputo Sense Fractional Order Derivative Model of Cholera
Authors: Sani Fakai Abubakar , Mohammed Olarenwaju Ibrahim
In Mathematics
A deterministic mathematical cholera model is formulated using ordinary differential equations. The formulated system of equations was then transformed into fractional derivative of Caputo sense, with order λ that ranges between 0 and 1. The transformed equations were displayed in Caputo sense fractional order derivative using the fractional derivative operator. These equations were then interpreted and the numerical Adams-Bashforth-Moulton kind of predictor-corrector method was used on maple 18 software to obtain the model’s outcome. Dynamics of cholera disease controls, comprising treatment, hygiene consciousness and vaccine were analyzed and the results were produced in graphs. The graphs show the dynamics of the susceptible, effects of vaccine on the susceptible and the rate of cholera infection. After studying and interpretation of the graphs, the result show that lower fractional order values in the range 0.25 to 0.5 gives lower values of susceptible and vaccinated individuals but gives higher number of infected individuals. To test efficiency of the obtained result, we compared it with the integer order derivative result, and found that the fractional order results gave a better and efficient, portray of the successful useable controls. Caputo sense fractional order derivative using Adams-Bashforth-Moulton kind of predictor-corrector numerical method, guaranteed getting result similar to Runge-Kutta fourth-order numerical method.
On An Illustrative Examples of a Studied Noetherity Dirac-Delta Extensions for a Noether Operator
Authors: Abdourahman , Ecclésiaste Tompé Weimbapou , Emmanuel Kengne , Shankishvili Lamara Dmitrievna
In Other, Mathematics
The purpose of this work is to illustrate by clear examples the noetherity nature of a finite Dirac-delta Extensions of a studied noether operator. Previously in our published papers, we have investigated in different two cases, the noetherization of a Dirac-delta extensions of a noether linear integro-differential operator defined by a third kind integral equation in some specific well chosen functional spaces. Our various already published researches were connected with such topic widely studied and clearly presenting different specific approaches, applied when establishing fundamentaly noether theory for some kind of integro-differential operators to reach the noetherization. The initial considered noether operator A has been extended with some finite dimensional spaces of Dirac-delta functions, and the noetherization of the two cases of extensions has been established depending with the parameters of the third kind integral equation defining A. The previous lead us to set the problem of the construction of practical examples clearly illustrating the relationship between theory and practise. For this aim, we based on an established wellknown noether theory and, we construct in this work step by step, two illustrative examples to show the interconnexion between the theory and pratise related to the investigation of the construction of noether theory for the considered extended noether operator denoted defined by a third kind linear singular integral equation in some generalized functional spaces. The extended operator A of the initial noether operator A is verified being also noether and therefore we deduce the index of the extended operator .