Theoretical and numerical analysis of a chaotic model with nonlocal and stochastic differential operators

İlknur Koca; Abdon Atangana

doi:10.11121/ijocta.2023.1398

Authors

İlknur Koca Department of Accounting and Financial Management, Seydikemer High School of Applied Sciences, Mugla Sıtkı Kocman University, Turkey https://orcid.org/0000-0003-4393-1588
Abdon Atangana Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa https://orcid.org/0000-0002-1886-3125

DOI:

https://doi.org/10.11121/ijocta.2023.1398

Keywords:

Nonlinear model, Chaotic number, Stochastic effect, Numerical analysis

Abstract

A set of nonlinear ordinary differential equations has been considered in this paper. The work tries to establish some theoretical and analytical insights when the usual time-deferential operator is replaced with the Caputo fractional derivative. Using the Caratheodory principle and other additional conditions, we established that the system has a unique system of solutions. A variety of well-known approaches were used to investigate the system. The stochastic version of this system was solved using a numerical approach based on Lagrange interpolation, and numerical simulation results were produced.

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Author Biographies

İlknur Koca, Department of Accounting and Financial Management, Seydikemer High School of Applied Sciences, Mugla Sıtkı Kocman University, Turkey

Ilknur Koca received the B.Sc. and M.Sc. degrees in 2007 and 2009 from the Department of Mathematics from Ankara University, Turkey respectively. She received her Ph.D. degree from the same university in 2013. She is working as an Associate Professor at the Department of Accounting and Financial Management, Seydikemer High School of Applied Sciences, Mugla Sıtkı Kocman University, Mugla, Turkey. Her research interests are methods and applications of partial and ordinary differential equations, fractional differential equations, and iterative methods.

Abdon Atangana, Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa

Abdon Atangana is a professor at the University of the Free State, Bloemfontein, South Africa.

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