Skip to main content
User Image

د.فردوس محمد عمر توفيق

Assistant Professor

عضو هيئة تدريس

كلية العلوم
مبنى 5، الدور الثالث، مكتب 46

Solutions of fractional-stochastic Bao’s system

Alexandria University Alexandria Engineering Journal

Systems of high-dimensional nonlinear ordinary differential equations play a significant role in Physics and applied sciences including big-data optimization, financial models, epidemic disease models. In this paper, we are concerned with numerical solutions of Bao’s system that is a 4-dimensional hyperchaotic system introduced by Bo-Cheng and Zhong (2008). We solve the Bao’s system with both the Crank-Nicolson and power series methods. Crank-Nicolson method is eventually evolved into a new system whose solution is presented in a quite neat algorithmic manner. By adding standard Brownian motion to each term in the model, we express the Bao’s system as a system of stochastic differential equations. We solve the stochastic system with an Euler-type approximate solution method. By adding noise and expressing time derivatives with Caputo-type fractional derivative, we study on synchronization and parameter estimation of the models. To the best of our knowledge, Bao’s system has not been numerically solved with the methods employed in this paper previously, and this paper considers fractional and stochastic Bao’s system for the first time in the history of research. Techniques employed by us in this paper may serve as a framework for solutions of many other systems of ordinary differential equations including Lorenz types and epidemic models.

Publication Work Type
original research
Publisher Name
Elsevier B.V.
Publishing City
Alexandria
Volume Number
Volume 59, Issue 6,
Magazine \ Newspaper
Alexandria Engineering Journal
Pages
Pages 4997-5006
more of publication
publications

Systems of high-dimensional nonlinear ordinary differential equations play a significant role in Physics and applied sciences including big-data optimization, financial models, epidemic disease…

by Mustafa Inc a,b , M.A. Akinlar c , F. Tchier d, *, C. Bal e , F. Bousbahi f , F.M.O. Tawfiq d , G.W. Weber
2020
Published in:
Elsevier B.V.
publications

Fractional-stochastic quadratic-cubic nonlinear Schro¨ dinger equation (QC-NLSE)
describing propagation of solitons through optical fibers is analyzed. Hermite transforms, white
noise…

by Zeliha Korpinar , , , Fairouz Tchier, Mustafa Inc , Fatiha Bousbahi , Ferdous M.O. Tawfiq, Mehmet Ali Akinlar
2020
publications

This paper is devoted to establishing some criteria for the existence of non-trivial
solutions for a class of fractional q-difference equations involving the p-Laplace operator,
which…

by Lakhdar Ragoub* , Fairouz Tchier, and Ferdous Tawfiq
2020