PubMed İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8650

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Now showing 1 - 8 of 8

Citation - WoS: 30
Citation - Scopus: 42
Caputo Sir Model for Covid-19 Under Optimized Fractional Order
(Springer, 2021) Ullah, Malik Z.; Baleanu, Dumitru; Alshomrani, Ali S.
Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case (nu=1). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.
Citation - WoS: 47
Citation - Scopus: 39
Existence of Solution and Stability for the Fractional Order Novel Coronavirus (ncov-2019) Model
(Springer, 2020) Baleanu, Dumitru; Adeel, Muhammad; Hussain, Azhar
The aim of this work is to present a new fractional order model of novel coronavirus (nCoV-2019) under Caputo-Fabrizio derivative. We make use of fixed point theory and Picard-Lindelof technique to explore the existence and uniqueness of solution for the proposed model. Moreover, we explore the generalized Hyers-Ulam stability of the model using Gronwall's inequality.
Citation - WoS: 158
Citation - Scopus: 192
A Fractional Differential Equation Model for the Covid-19 Transmission by Using the Caputo-Fabrizio Derivative
(Springer, 2020) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.
Citation - WoS: 29
Citation - Scopus: 33
Fractional Unit-Root Tests Allowing for a Fractional Frequency Flexible Fourier Form Trend: Predictability of Covid-19
(Springer, 2021) Omay, Tolga; Baleanu, Dumitru
In this study we propose a fractional frequency flexible Fourier form fractionally integrated ADF unit-root test, which combines the fractional integration and nonlinear trend as a form of the Fourier function. We provide the asymptotics of the newly proposed test and investigate its small-sample properties. Moreover, we show the best estimators for both fractional frequency and fractional difference operator for our newly proposed test. Finally, an empirical study demonstrates that not considering the structural break and fractional integration simultaneously in the testing process may lead to misleading results about the stochastic behavior of the Covid-19 pandemic.
Citation - WoS: 1
Citation - Scopus: 2
Higher-Dimensional Physical Models With Multimemory Indices: Analytic Solution and Convergence Analysis
(Springer, 2020) Alquran, Marwan; Abdel-Muhsen, Ruwa; Momani, Shaher; Baleanu, Dumitru; Jaradat, Imad
The purpose of this work is to analytically simulate the mutual impact for the existence of both temporal and spatial Caputo fractional derivative parameters in higher-dimensional physical models. For this purpose, we employ the gamma_-Maclaurin series along with an amendment of the power series technique. To supplement our idea, we present the necessary convergence analysis regarding the gamma_-Maclaurin series. As for the application side, we solved versions of the higher-dimensional heat and wave models with spatial and temporal Caputo fractional derivatives in terms of a rapidly convergent gamma_-Maclaurin series. The method performed extremely well, and the projections of the obtained solutions into the integer space are compatible with solutions available in the literature. Finally, the graphical analysis showed a possibility that the Caputo fractional derivatives reflect some memory characteristics.
Citation - WoS: 39
Citation - Scopus: 45
The Mean Value Theorem and Taylor's Theorem for Fractional Derivatives With Mittag-Leffler Kernel
(Pushpa Publishing House, 2018) Baleanu, Dumitru; Fernandez, Arran
We establish analogues of the mean value theorem and Taylor's theorem for fractional differential operators defined using a Mittag-Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.
Citation - WoS: 17
Citation - Scopus: 21
Modeling the Transmission Dynamics of Delayed Pneumonia-Like Diseases With a Sensitivity of Parameters
(Springer, 2021) Baleanu, Dumitru; Raza, Ali; Rafiq, Muhammad; Soori, Atif Hassan; Mohsin, Muhammad; Naveed, Muhammad
Pneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. In 2017, 0.88 million children were killed under the age of five years. An analysis of pneumonia disease is performed with the help of a delayed mathematical modelling technique. The epidemiological system contemplates subpopulations of susceptible, carriers, infected and recovered individuals, along with nonlinear interactions between the members of those subpopulations. The positivity and the boundedness of the ongoing problem for nonnegative initial data are thoroughly proved. The system possesses pneumonia-free and pneumonia existing equilibrium points, whose stability is studied rigorously. Moreover, the numerical simulations confirm the validity of these theoretical results.
Citation - WoS: 18
Citation - Scopus: 21
On the Optimal Control of Coronavirus (2019-Ncov) Mathematical Model; a Numerical Approach
(Springer, 2020) Al-Mekhlafi, S. M.; Albalawi, A. O.; Baleanu, D.; Sweilam, N. H.
In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grunwald-Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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