Browsing by Author "Qureshi, Sania"

Now showing 1 - 7 of 7

Citation - WoS: 15
Citation - Scopus: 16
A New Three-Step Root-Finding Numerical Method and Its Fractal Global Behavior
(Mdpi, 2021) Tassaddiq, Asifa; Baleanu, Dumitru; Qureshi, Sania; Soomro, Amanullah; Hincal, Evren; Baleanu, Dumitru; Shaikh, Asif Ali; 56389; Matematik
There is an increasing demand for numerical methods to obtain accurate approximate solutions for nonlinear models based upon polynomials and transcendental equations under both single and multivariate variables. Keeping in mind the high demand within the scientific literature, we attempt to devise a new nonlinear three-step method with tenth-order convergence while using six functional evaluations (three functions and three first-order derivatives) per iteration. The method has an efficiency index of about 1.4678, which is higher than most optimal methods. Convergence analysis for single and systems of nonlinear equations is also carried out. The same is verified with the approximated computational order of convergence in the absence of an exact solution. To observe the global fractal behavior of the proposed method, different types of complex functions are considered under basins of attraction. When compared with various well-known methods, it is observed that the proposed method achieves prespecified tolerance in the minimum number of iterations while assuming different initial guesses. Nonlinear models include those employed in science and engineering, including chemical, electrical, biochemical, geometrical, and meteorological models.
Citation - WoS: 176
Citation - Scopus: 190
Fractional modeling of blood ethanol concentration system with real data application
(Amer inst Physics, 2019) Qureshi, Sania; Baleanu, Dumitru; Yusuf, Abdullahi; Shaikh, Asif Ali; Inc, Mustafa; Baleanu, Dumitru; 56389; Matematik
In this study, a physical system called the blood ethanol concentration model has been investigated in its fractional (non-integer) order version. The three most commonly used fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu fractional derivative in the Caputo sense-ABC and the Caputo-Fabrizio-CF) kernels have been used to fractionalize the model, whereas during the process of fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of squared residuals is carried out to show the performance of the models along with some graphical illustrations. Published under license by AIP Publishing.
Citation - WoS: 18
Citation - Scopus: 22
IMPACT OF PUBLIC HEALTH AWARENESS PROGRAMS ON COVID-19 DYNAMICS: A FRACTIONAL MODELING APPROACH
(World Scientific Publ Co Pte Ltd, 2023) Zafar, Zain ul abadin; Baleanu, Dumitru; Yusuf, Abdullahi; Musa, Salihu s.; Qureshi, Sania; Alshomrani, Ali s.; Baleanu, Dumitru; 56389; Matematik
Public health awareness programs have been a crucial strategy in mitigating the spread of emerging and re-emerging infectious disease outbreaks of public health significance such as COVID-19. This study adopts an Susceptible-Exposed-Infected-Recovered (SEIR) based model to assess the impact of public health awareness programs in mitigating the extent of the COVID-19 pandemic. The proposed model, which incorporates public health awareness programs, uses ABC fractional operator approach to study and analyze the transmission dynamics of SARS-CoV-2. It is possible to completely understand the dynamics of the model's features because of the memory effect and hereditary qualities that exist in the fractional version. The fixed point theorem has been used to prove the presence of a unique solution, as well as the stability analysis of the model. The nonlinear least-squares method is used to estimate the parameters of the model based on the daily cumulative cases of the COVID-19 pandemic in Nigeria from March 29 to June 12, 2020. Through the use of simulations, the model's best-suited parameters and the optimal ABC fractional-order parameter t may be determined and optimized. The suggested model is proved to understand the virus's dynamical behavior better than the integer-order version. In addition, numerous numerical simulations are run using an efficient numerical approach to provide further insight into the model's features.
Citation - WoS: 44
Citation - Scopus: 41
Mathematical modeling for adsorption process of dye removal nonlinear equation using power law and exponentially decaying kernels
(Amer inst Physics, 2020) Qureshi, Sania; Baleanu, Dumitru; Yusuf, Abdullahi; Shaikh, Asif Ali; Inc, Mustafa; Baleanu, Dumitru; 56389; Matematik
In this research work, a new time-invariant nonlinear mathematical model in fractional (non-integer) order settings has been proposed under three most frequently employed strategies of the classical Caputo, the Caputo-Fabrizio, and the Atangana-Baleanu-Caputo with the fractional parameter chi , where 0 < chi <= 1. The model consists of a nonlinear autonomous transport equation used to study the adsorption process in order to get rid of the synthetic dyeing substances from the wastewater effluents. Such substances are used at large scale by various industries to color their products with the textile and chemical industries being at the top. The non-integer-order model suggested in the present study depicts the past behavior of the concentration of the solution on the basis of having information of the initial concentration present in the dye. Being nonlinear, it carries the possibility to have no exact solution. However, the Lipchitz condition shows the existence and uniqueness of the underlying model's solution in non-integer-order settings. From a numerical simulation viewpoint, three numerical techniques having first order convergence have been employed to illustrate the numerical results obtained. Published under license by AIP Publishing.
Citation - WoS: 81
Citation - Scopus: 79
New Numerical Aspects of Caputo-Fabrizio Fractional Derivative Operator
(Mdpi, 2019) Qureshi, Sania; Baleanu, Dumitru; Rangaig, Norodin A.; Baleanu, Dumitru; 56389; Matematik
In this paper, a new definition for the fractional order operator called the Caputo-Fabrizio (CF) fractional derivative operator without singular kernel has been numerically approximated using the two-point finite forward difference formula for the classical first-order derivative of the function f (t) appearing inside the integral sign of the definition of the CF operator. Thus, a numerical differentiation formula has been proposed in the present study. The obtained numerical approximation was found to be of first-order convergence, having decreasing absolute errors with respect to a decrease in the time step size h used in the approximations. Such absolute errors are computed as the absolute difference between the results obtained through the proposed numerical approximation and the exact solution. With the aim of improved accuracy, the two-point finite forward difference formula has also been utilized for the continuous temporal mesh. Some mathematical models of varying nature, including a diffusion-wave equation, are numerically solved, whereas the first-order accuracy is not only verified by the error analysis but also experimentally tested by decreasing the time-step size by one order of magnitude, whereupon the proposed numerical approximation also shows a one-order decrease in the magnitude of its absolute errors computed at the final mesh point of the integration interval under consideration.
Citation - WoS: 117
Citation - Scopus: 119
Two-strain epidemic model involving fractional derivative with Mittag-Leffler kernel
(Aip Publishing, 2018) Yusuf, Abdullahi; Baleanu, Dumitru; Qureshi, Sania; Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Shaikh, Asif Ali; 56389; Matematik
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.
Citation - WoS: 2
Citation - Scopus: 4
Variable Stepsize Construction of a Two-Step Optimized Hybrid Block Method With Relative Stability
(de Gruyter Poland Sp Z O O, 2022) Baleanu, Dumitru; Qureshi, Sania; Soomro, Amanullah; Shaikh, Asif Ali; Matematik
Several numerical techniques for solving initial value problems arise in physical and natural sciences. In many cases, these problems require numerical treatment to achieve the required solution. However, in today's modern era, numerical algorithms must be cost-effective with suitable convergence and stability features. At least the fifth-order convergent two-step optimized hybrid block method recently proposed in the literature is formulated in this research work with its variable stepsize approach for numerically solving first- and higher-order initial-value problems in ordinary differential equations. It has been constructed using a continuous approximation achieved through interpolation and collocation techniques at two intra-step points chosen by optimizing the local truncation errors of the main formulae. The theoretical analysis, including order stars for the relative stability, is considered. Both fixed and variable stepsize approaches are presented to observe the superiority of the latter approach. When tested on challenging differential systems, the method gives better accuracy, as revealed by the efficiency plots and the error distribution tables, including the machine time measured in seconds.