Olusola Kolebaje

Bio: Olusola Kolebaje is an academic researcher from Adeyemi College of Education. The author has contributed to research in topics: Nonlinear system & Adomian decomposition method. The author has an hindex of 7, co-authored 25 publications receiving 138 citations. Previous affiliations of Olusola Kolebaje include Redeemer's University & University of Ibadan.

Chaos in a calcium oscillation model via Atangana-Baleanu operator with strong memory

Abstract: Calcium oscillations have a significant importance in gesturing messengers for a wide variety of cells because cells exhibit calcium oscillations in response to external stimulation. The significance of the calcium oscillations vividly attract researchers, this is due to the empirical, numerical or experimental analyses on calcium oscillations and the lack of modern fractional techniques. An analytic study of chaotic behavior in the calcium oscillation model is carried out through fractional and non-fractional techniques. The governing non-linear differential equations of calcium oscillations have been established through newly defined Atangana-Baleanu fractional operators. In order to analyze the dynamics of the fractional calcium oscillation model, powerful techniques are applied to the governing non-linear fractional differential equations namely the (Laplace transform and modified homotopy perturbation transform method MHATM). The newly defined Atangana-Baleanu fractional approach is examined for the parameters that show periodic doubling and route to chaos. Finally, several similarities and differences have been underlined due to the fractional-order effect for the calcium oscillations with chaotic region at different scale.

Fractional investigations of zoonotic visceral leishmaniasis disease with singular and non-singular kernel

Abstract: Memory has a great impact to study the dynamics of any real epidemic process in a better way. An epidemic model including memory effect is governed by fractional differential equations. In the present paper we explore the dynamics of the zoonotic visceral leishmaniasis (ZVL) disease using fractional derivative in both the Caputo and Atangana-Baleanu sense. The proposed model in the Caputo sense is solved by the well-known method known as modified differential transform method (MDTM), which is efficient and reliable. Further, the solution for the model with Atangana-Baleanu derivative is obtained by the modified Adams-Bashforh method. Numerical simulations are presented by using a different value of the fractional order parameter $ \alpha$ . The numerical results obtained through the MDTM and the modified Adams-Bashforh method are reasonable and provide useful information in the non-integer case. Numerical results presented for the fractional order parameter $ \alpha$ and in the integer case for the Caputo derivative model are compared with the Runge-Kutta method which gives good agreement. The application of Atangana-Baleanu derivative, the Caputo derivative and the use of the numerical approaches, MDTM, Adams Bashforth and the Runge-Kutta method (for the integer case) for an epidemic model is a novel practice and provides more flexible and deeper information about the complexity of the dynamics of ZVL.

Numerical Solution of the Korteweg De Vries Equation by Finite Difference and Adomian Decomposition Method

Abstract: The Korteweg de Vries (KDV) equation which is a non-linear PDE plays an important role in studying the propagation of low amplitude water waves in shallow water bodies, the solution to this equation leads to solitary waves or solitons. In this paper, we present the analytic solution and use the explicit and implicit finite difference schemes and the Adomian decomposition method to obtain approximate solutions to the KDV equation. As the behavior of the solitons generated from the KDV depends on the nature of the initial wave, this work aims to study two possible scenarios (hyperbolic tangent initial condition and a sinusoidal initial condition) and obtained solution analytically, numerically with the aforementioned methods. Comparison between the four different solutions is done with the aid of tables and diagrams. We observed that valid analytical solutions for the KDV equation are restricted to time values close to the initial time and that the Adomian decomposition method is a wonderful tool for solving the KDV equation and other non-linear PDEs.

Estimating solar radiation in ikeja and port harcourt via correlation with relative humidity and temperature

Abstract: Relative humidity and temperature data are more readily available to obtain from observatories than sunshine hour data. In this work, 10 years (1986–1987, 1990–1997) monthly average measurement of relative solar radiation, daily temperature range, relative humidity and the ratio of minimum to maximum temperature were used to establish the coefficient of eight models for estimating solar radiation in Ikeja and Port Harcourt. Coefficient of correlation (R), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), t-statistic and the rank score were used as performance indicators. In Port Harcourt, the equation producing the best result with MBE, RMSE, MPE and t- statistic value of −0.1078, 0.9850, −0.4373% and 0.3653, respectively, is given by: R R

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative

Abstract: The present paper describes the mathematical modeling and dynamics of a novel corona virus (2019-nCoV). We describe the brief details of interaction among the bats and unknown hosts, then among the peoples and the infections reservoir (seafood market). The seafood marked are considered the main source of infection when the bats and the unknown hosts (may be wild animals) leaves the infection there. The purchasing of items from the seafood market by peoples have the ability to infect either asymptomatically or symptomatically. We reduced the model with the assumptions that the seafood market has enough source of infection that can be effective to infect people. We present the mathematical results of the model and then formulate a fractional model. We consider the available infection cases for January 21, 2020, till January 28, 2020 and parameterized the model. We compute the basic reproduction number for the data is R 0 ≈ 2.4829 . The fractional model is then solved numerically by presenting many graphical results, which can be helpful for the infection minimization.

Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation

Abstract: In this paper, we study on the conformable (2+1)-dimensional Ablowitz-KaupNewell-Segur equation in order to show the existence of complex combined dark-bright soliton solutions. To this purpose an effective method which is the sine-Gordon expansion method is used. The 2D and 3D surfaces under some suitable values of parameters are also plotted.

The dynamics of COVID-19 with quarantined and isolation

Abstract: In the present paper, we formulate a new mathematical model for the dynamics of COVID-19 with quarantine and isolation. Initially, we provide a brief discussion on the model formulation and provide relevant mathematical results. Then, we consider the fractal-fractional derivative in Atangana–Baleanu sense, and we also generalize the model. The generalized model is used to obtain its stability results. We show that the model is locally asymptotically stable if $\mathcal{R}_{0}<1$ . Further, we consider the real cases reported in China since January 11 till April 9, 2020. The reported cases have been used for obtaining the real parameters and the basic reproduction number for the given period, $\mathcal{R}_{0}\approx 6.6361$ . The data of reported cases versus model for classical and fractal-factional order are presented. We show that the fractal-fractional order model provides the best fitting to the reported cases. The fractional mathematical model is solved by a novel numerical technique based on Newton approach, which is useful and reliable. A brief discussion on the graphical results using the novel numerical procedures are shown. Some key parameters that show significance in the disease elimination from the society are explored.