Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 8Citation - Scopus: 8On Solutions of the Stiff Differential Equations in Chemistry Kinetics With Fractal-Fractional Derivatives(Asme, 2022) Aslam, Muhammad; Akgul, Ali; Jarad, Fahd; Farman, MuhammadIn this paper, we consider the stiff systems of ordinary differential equations arising from chemistry kinetics. We develop the fractional order model for chemistry kinetics problems by using the new fractal operator such as fractal fractional and Atangana-Toufik scheme. Recently a deep concept of fractional differentiation with nonlocal and nonsingular kernel was introduced to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. Many scientific results are presented in the paper and also prove these results by effective numerical results. These concepts are very important to use for real-life problems like Brine tank cascade, Recycled Brine tank cascade, pond pollution, home heating, and biomass transfer problem. These results are very important for solving the nonlinear model in chemistry kinetics which will be helpful to understand the chemical reactions and their actual behavior; also the observation can be developed for future kinematic chemical reactions with the help of these results.Article Citation - WoS: 48Citation - Scopus: 57Modelling and Analysis of a Measles Epidemic Model With the Constant Proportional Caputo Operator(Mdpi, 2023) Shehzad, Aamir; Akgul, Ali; Baleanu, Dumitru; De la Sen, Manuel; Farman, Muhammad; Sen, Manuel De laDespite the existence of a secure and reliable immunization, measles, also known as rubeola, continues to be a leading cause of fatalities globally, especially in underdeveloped nations. For investigation and observation of the dynamical transmission of the disease with the influence of vaccination, we proposed a novel fractional order measles model with a constant proportional (CP) Caputo operator. We analysed the proposed model's positivity, boundedness, well-posedness, and biological viability. Reproductive and strength numbers were also verified to examine how the illness dynamically behaves in society. For local and global stability analysis, we introduced the Lyapunov function with first and second derivatives. In order to evaluate the fractional integral operator, we used different techniques to invert the PC and CPC operators. We also used our suggested model's fractional differential equations to derive the eigenfunctions of the CPC operator. There is a detailed discussion of additional analysis on the CPC and Hilfer generalised proportional operators. Employing the Laplace with the Adomian decomposition technique, we simulated a system of fractional differential equations numerically. Finally, numerical results and simulations were derived with the proposed measles model. The intricate and vital study of systems with symmetry is one of the many applications of contemporary fractional mathematical control. A strong tool that makes it possible to create numerical answers to a given fractional differential equation methodically is symmetry analysis. It is discovered that the proposed fractional order model provides a more realistic way of understanding the dynamics of a measles epidemic.Article Citation - WoS: 23Citation - Scopus: 26Epidemiological Analysis of the Coronavirus Disease Outbreak With Random Effects(Tech Science Press, 2021) Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Naeem, Muhammad; Baleanu, Dumitru; Farman, MuhammadToday, coronavirus appears as a serious challenge to the whole world. Epidemiological data of coronavirus is collected through media and web sources for the purpose of analysis. New data on COVID-19 are available daily, yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited, and uncertainty remains around nearly all its parameters' values. This research provides the scientific and public health communities better resources, knowledge, and tools to improve their ability to control the infectious diseases. Using the publicly available data on the ongoing pandemic, the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 infections. Formulation of the testing hypotheses for different countries with a 95% level of confidence, and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different countries. The results will be helpful in decision making as well as in further mathematical analysis and control strategy. Statistical tools are used to investigate this pandemic, which will be useful for further research. The testing of the hypothesis is done for the differences in various effects including standard errors. Changes in states' variables are observed over time. The rapid outbreak of coronavirus can be stopped by reducing its transmission. Susceptible should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.Article Citation - WoS: 29Citation - Scopus: 33Dynamical Transmission of Coronavirus Model With Analysis and Simulation(Tech Science Press, 2021) Baleanu, Dumitru; Akgul, Ali; Ahmad, Aqeel; Saleem, Muhammad Umer; Farman, MuhammadCOVID-19 acts as a serious challenge to the whole world. Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease. We analyze the diseases free and endemic equilibrium point including stability of the model. The certain threshold value of the basic reproduction number R-0 is found to observe whether population is in disease free state or endemic state. Moreover, the epidemic peak has been obtained and we expect a considerable number of cases. Finally, some numerical results are presented which show the effect of parameters estimation and different step size on our obtained solutions at the real data of some countries to check the actual behavior of the COVID-19 at different countries.Article Citation - WoS: 234Citation - Scopus: 302On a Fractional Operator Combining Proportional and Classical Differintegrals(Mdpi, 2020) Fernandez, Arran; Akgul, Ali; Baleanu, DumitruThe Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviours by fractional differential equations. It is defined, for a differentiable function <mml:semantics>f(t)</mml:semantics>, by a fractional integral operator applied to the derivative <mml:semantics>f ' (t)</mml:semantics>. We define a new fractional operator by substituting for this <mml:semantics>f ' (t)</mml:semantics> a more general proportional derivative. This new operator can also be written as a Riemann-Liouville integral of a proportional derivative, or in some important special cases as a linear combination of a Riemann-Liouville integral and a Caputo derivative. We then conduct some analysis of the new definition: constructing its inverse operator and Laplace transform, solving some fractional differential equations using it, and linking it with a recently described bivariate Mittag-Leffler function.Article Citation - WoS: 4Citation - Scopus: 6New Numerical Method for Solving Tenth Order Boundary Value Problems(Mdpi, 2018) Akgul, Esra Karatas; Baleanu, Dumitru; Inc, Mustafa; Akgul, AliIn this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain some useful reproducing kernel functions to get approximate solutions. We obtain very efficient results by this method. We show our numerical results by tables.Article Citation - WoS: 15Citation - Scopus: 16Solving the Lane-Emden Equation Within a Reproducing Kernel Method and Group Preserving Scheme(Mdpi, 2017) Akgul, Ali; Inc, Mustafa; Mustafa, Idrees Sedeeq; Baleanu, Dumitru; Hashemi, Mir SajjadWe apply the reproducing kernel method and group preserving scheme for investigating the Lane-Emden equation. The reproducing kernel method is implemented by the useful reproducing kernel functions and the numerical approximations are given. These approximations demonstrate the preciseness of the investigated techniques.Article Citation - WoS: 15Citation - Scopus: 21On the Solutions of Electrohydrodynamic Flow With Fractional Differential Equations by Reproducing Kernel Method(de Gruyter Open Ltd, 2016) Baleanu, Dumitru; Inc, Mustafa; Tchier, Fairouz; Akgul, AliIn this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model. Obtained results prove that the reproducing kernel method (RKM) is very effective. We obtain good results without any transformation or discretization. Numerical experiments on test examples show that our proposed schemes are of high accuracy and strongly support the theoretical results.