PubMed İndeksli Yayınlar Koleksiyonu

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

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Citation - WoS: 34
Citation - Scopus: 39
Design 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 Krishna
Investigation 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.
Citation - WoS: 2
Existence 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 Publishing
Citation - WoS: 203
Citation - Scopus: 210
On Exact Traveling-Wave Solutions for Local Fractional Korteweg-De Vries Equation
(Aip Publishing, 2016) Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo; Yang, Xiao-Jun
This 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.
Citation - WoS: 107
Citation - Scopus: 118
On the Analysis of Chemical Kinetics System Pertaining To a Fractional Derivative With Mittag-Leffler Type Kernel
(Aip Publishing, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
The 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.
Citation - WoS: 37
Citation - Scopus: 37
Riesz Riemann-Liouville Difference on Discrete Domains
(Aip Publishing, 2016) Baleanu, Dumitru; Xie, He-Ping; Wu, Guo-Cheng
A 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.
Citation - WoS: 30
Citation - Scopus: 32
Spatio-Temporal Numerical Modeling of Reaction-Diffusion Measles Epidemic System
(Aip Publishing, 2019) Wei, Zhouchao; Baleanu, Dumitru; Rafiq, M.; Rehman, M. A.; Ahmed, Nauman
In 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.
Citation - WoS: 123
Citation - Scopus: 124
Two-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, Abdullahi
In 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.

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