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Article Citation - WoS: 3Citation - Scopus: 9Artificial Intelligence Computing Analysis of Fractional Order Covid-19 Epidemic Model(Aip Publishing, 2023) Baleanu, Dumitru; Cheema, Tahir Nawaz; Fadhal, Emad; Ibrahim, Rashid I. H.; Abdelli, Nouara; Raza, AliArtificial intelligence plays a very prominent role in many fields, and of late, this term has been gaining much more popularity due to recent advances in machine learning. Machine learning is a sphere of artificial intelligence where machines are responsible for doing daily chores and are believed to be more intelligent than humans. Furthermore, artificial intelligence is significant in behavioral, social, physical, and biological engineering, biomathematical sciences, and many more disciplines. Fractional-order modeling of a real-world problem is a powerful tool for understanding the dynamics of the problem. In this study, an investigation into a fractional-order epidemic model of the novel coronavirus (COVID-19) is presented using intelligent computing through Bayesian-regularization backpropagation networks (BRBFNs). The designed BRBFNs are exploited to predict the transmission dynamics of COVID-19 disease by taking the dataset from a fractional numerical method based on the Grunwald-Letnikov backward finite difference. The datasets for the fractional-order mathematical model of COVID-19 for Wuhan and Karachi metropolitan cities are trained with BRBFNs for biased and unbiased input and target values. The proposed technique (BRBFNs) is implemented to estimate the integer and fractional-order COVID-19 spread dynamics. Its reliability, effectiveness, and validation are verified through consistently achieved accuracy metrics that depend on error histograms, regression studies, and mean squared error.Article Citation - WoS: 33Citation - Scopus: 38Design of a Fractional-Order Atmospheric Model Via a Class of Act-Like Chaotic System and Its Sliding Mode Chaos Control(Aip Publishing, 2023) Baishya, Chandrali; Veeresha, Pundikala; Baleanu, Dumitru; Naik, Manisha KrishnaInvestigation of the dynamical behavior related to environmental phenomena has received much attention across a variety of scientific domains. One such phenomenon is global warming. The main causes of global warming, which has detrimental effects on our ecosystem, are mainly excess greenhouse gases and temperature. Looking at the significance of this climatic event, in this study, we have connected the ACT-like model to three climatic components, namely, permafrost thaw, temperature, and greenhouse gases in the form of a Caputo fractional differential equation, and analyzed their dynamics. The theoretical aspects, such as the existence and uniqueness of the obtained solution, are examined. We have derived two different sliding mode controllers to control chaos in this fractional-order system. The influences of these controllers are analyzed in the presence of uncertainties and external disturbances. In this process, we have obtained a new controlled system of equations without and with uncertainties and external disturbances. Global stability of these new systems is also established. All the aspects are examined for commensurate and non-commensurate fractional-order derivatives. To establish that the system is chaotic, we have taken the assistance of the Lyapunov exponent and the bifurcation diagram with respect to the fractional derivative. To perform numerical simulation, we have identified certain values of the parameters where the system exhibits chaotic behavior. Then, the theoretical claims about the influence of the controller on the system are established with the help of numerical simulations.Article Citation - WoS: 5Citation - Scopus: 5Dynamical Analysis of a Class of Seir Models Through Delayed Strategies(Aip Publishing, 2023) Rafiq, Muhammad; Ahmed, Nauman; Baleanu, Dumitru; Alfwzan, Wafa F.; Raza, AliIn recent decades, the mathematical modeling of infectious diseases, real-world problems, non-linear dynamical complex systems, etc., has increased significantly. According to World Health Organization, tobacco use is the cause of about 22% of cancer deaths. Another 10% are due to obesity, poor diet, lack of physical activity, and excessive drinking of alcohol. Approximately 5%-10% of cancers are due to inherited genetic defects. The objective is to investigate the impact of time delays in implementing control measures on the epidemic dynamics. The classification of cell population has four compartments: susceptible cells (x), cancer-infected cells (y), virus-free cells (v), and immune cells (z). Our focus is to find the equilibria of the problem and their stability. The stability of the solutions is of two types: locally asymptotic and globally asymptotic. The Routh-Hurwitz criterion, Volterra-type Lyapunov function, and LaSalle's invariance principle are used to verify the stability of solutions. The graphical behavior depicts the stable solutions to a real-world problem and supports the stability analysis of the problem. The findings contribute to the understanding of epidemic dynamics and provide valuable information for designing and implementing effective intervention strategies in public health systems.Article Citation - WoS: 4Citation - Scopus: 3Evolutionary Computational Method for Tuberculosis Model With Fuzziness(Aip Publishing, 2023) Dayan, Fazal; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Raza, Ali; Alsaadi, AteqThis work investigates the computational study of a six-compartmental mathematical model of tuberculosis disease dynamics with the impact of vaccination. Traditional mathematical models presume that all variables are precise and can be measured or calculated precisely. However, in many real-world scenarios, variables may need to be more accurate or easier to quantify, resulting in model uncertainty. Considering this, fuzziness is introduced into the model by taking the contact, recovery, and death rates due to disease as fuzzy membership functions. Two numerical computational schemes, forward Euler and nonstandard finite difference (NSFD), are designed to solve the model. The positivity and convergence for the developed method are investigated, which are significant characteristics of these dynamical models, and it is revealed that these features are preserved in the extended scheme. Numerical computations are performed to support the analytical results. The numerical and computational results indicate that the proposed NSFD method adequately represents the dynamics of the disease despite the uncertainty and heterogeneity. Moreover, the obtained method generates plausible predictions that regulators can use to design and develop control strategies to support decision-making.Article Citation - WoS: 2Existence of Measure Pseudo-Almost Automorphic Functions and Applications To Impulsive Integro-Differential Equation(Aip Publishing, 2021) Baleanu, Dumitru; George, Soumya; Grayna, J.; Kavitha, V.This article's main objective is to establish the measure pseudo-almost automorphic solution of an integro-differential equation with impulses. We develop the existence results based on the Banach contraction principle mapping and Krasnoselskii and Krasnoselskii-Schaefer type fixed point theorems. Finally, some examples are given to illustrate the significance of our theoretical findings.Published under an exclusive license by AIP PublishingArticle Citation - WoS: 68Citation - Scopus: 69Fractional Hamiltonian Analysis of Higher Order Derivatives Systems(Aip Publishing, 2006) Tas, Kenan; Baleanu, Dumitru; Muslih, Sami I.The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives. (c) 2006 American Institute of Physics.Article Citation - Scopus: 1Global Stability, Periodicity, and Bifurcation Analysis of a Difference Equation(Aip Publishing, 2023) Manuel, M. Maria Susai; Baleanu, Dumitru; Dilip, D. S.; Amalraj, J. LeoThis research aims to discuss the existence, global stability, periodicity, and bifurcation analysis of a modified version of the ecological model proposed by Tilman and Wedlin [Nature 353, 653-655 (1991)].Article Citation - WoS: 203Citation - Scopus: 210On Exact Traveling-Wave Solutions for Local Fractional Korteweg-De Vries Equation(Aip Publishing, 2016) Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo; Yang, Xiao-JunThis paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces. Published by AIP Publishing.Article Citation - WoS: 107Citation - Scopus: 118On the Analysis of Chemical Kinetics System Pertaining To a Fractional Derivative With Mittag-Leffler Type Kernel(Aip Publishing, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, JagdevThe pivotal aim of this paper was to analyze a new fractional model of chemical kinetics system related to a newly discovered Atangana-Baleanu derivative with fractional order having non-singular and non-local kernel. The numerical solution is derived by making use of the iterative scheme. The existence of the solution of chemical kinetics system of arbitrary order is examined by implementing the fixed-point theorem. The uniqueness of the special solution of the studied model is shown. The effect of different variables and order of arbitrary ordered derivative on concentrations is demonstrated in tabular and graphical forms. The numerical results for chemical kinetics system pertaining to the newly derivative with fractional order are compared with the chemical kinetics system involving classical derivative. Published by AIP Publishing.Article Citation - WoS: 16Citation - Scopus: 18On the Asymptotic Integration of a Class of Sublinear Fractional Differential Equations(Aip Publishing, 2009) Mustafa, Octavian G.; Baleanu, DumitruWe estimate the growth in time of the solutions to a class of nonlinear fractional differential equations D-0+(alpha)(x-x(0))=f(t,x) which includes D-0+(alpha)(x-x(0))=H(t)x(lambda) with lambda is an element of(0,1) for the case of slowly decaying coefficients H. The proof is based on the triple interpolation inequality on the real line and the growth estimate reads as x(t)=o(t(a alpha)) when t ->+infinity for 1>alpha>1-a>lambda>0. Our result can be thought of as a noninteger counterpart of the classical Bihari asymptotic integration result for nonlinear ordinary differential equations. By a carefully designed example we show that in some circumstances such an estimate is optimal.Article Citation - WoS: 37Citation - Scopus: 37Riesz Riemann-Liouville Difference on Discrete Domains(Aip Publishing, 2016) Baleanu, Dumitru; Xie, He-Ping; Wu, Guo-ChengA Riesz difference is defined by the use of the Riemann-Liouville differences on time scales. Then the definition is considered for discrete fractional modelling. A lattice fractional equation method is proposed among which the space variable is defined on discrete domains. Finite memory effects are introduced into the lattice system and the numerical formulae are given. Adomian decomposition method is adopted to solve the fractional partial difference equations numerically. Published by AIP Publishing.Article Citation - WoS: 30Citation - Scopus: 32Spatio-Temporal Numerical Modeling of Reaction-Diffusion Measles Epidemic System(Aip Publishing, 2019) Wei, Zhouchao; Baleanu, Dumitru; Rafiq, M.; Rehman, M. A.; Ahmed, NaumanIn this work, we investigate the numerical solution of the susceptible exposed infected and recovered measles epidemic model. We also evaluate the numerical stability and the bifurcation value of the transmission parameter from susceptibility to a disease of the proposed epidemic model. The proposed method is a chaos free finite difference scheme, which also preserves the positivity of the solution of the given epidemic model. Published under license by AIP Publishing.Article Citation - WoS: 123Citation - Scopus: 124Two-Strain Epidemic Model Involving Fractional Derivative With Mittag-Leffler Kernel(Aip Publishing, 2018) Qureshi, Sania; Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Shaikh, Asif Ali; Yusuf, AbdullahiIn the present study, the fractional version with respect to the Atangana-Baleanu fractional derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu fractional derivative operator in the caputo sense. To believe upon the results obtained, the fractional order alpha has been allowed to vary between (0, 1], whereupon the physical observations match with those obtained in the classical case, but the fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of fractional order derivatives for ABC. Finally, the fractional forward Euler method in the classical caputo sense has been used to illustrate the better performance of the numerical method obtained via the Atangana-Baleanu fractional derivative operator in the caputo sense. Published by AIP Publishing.
