Browsing by Author "Farman, Muhammad"

Now showing 1 - 8 of 8

Citation - WoS: 20
Citation - Scopus: 25
Analysis of a fractional order Bovine Brucellosis disease model with discrete generalized Mittag–Leffler kernels
(Elsevier, 2023) Farman, Muhammad; Baleanu, Dumitru; Shehzad, Aamir; Akgul, Ali; Baleanu, Dumitru; Attia, Nourhane; Hassan, Ahmed M.; 56389; Matematik
Bovine Brucellosis, a zoonotic disease, can infect cattle in tropical and subtropical areas. It remains a critical issue for both human and animal health in many parts of the world, especially those where livestock is an important source of food and income. An efficient method for monitoring the illness's increasing prevalence and developing low-cost prevention strategies for both its effects and recurrence is brucellosis disease modeling. We create a fractional-order model of Bovine Brucellosis using a discrete modified Atangana-Baleanu fractional difference operator of the Liouville-Caputo type. An analysis of the suggested system's well-posedness and a qualitative investigation are both conducted. The examination of the Volterra-type Lyapunov function for global stability is supported by the first and derivative tests. The Lipschitz condition is also used for the model in order to meet the criterion of the uniqueness of the exact solution. We created an endemic and disease-free equilibrium. Solutions are built in the discrete generalized form of the Mittag-Leffler kernel in order to analyze the effect of the fractional operator with numerical simulations and emphasize the effects of the sickness due to the many factors involved. The capacity of the suggested model to forecast an infectious disease like brucellosis can help researchers and decision-makers take preventive actions.
Citation - WoS: 32
Citation - Scopus: 36
Analysis of Fractional Order Chaotic Financial Model with Minimum Interest Rate Impact
(Mdpi, 2020) Farman, Muhammad; Baleanu, Dumitru; Akgul, Ali; Baleanu, Dumitru; Imtiaz, Sumaiyah; Ahmad, Aqeel; 56389; Matematik
The main objective of this paper is to construct and test fractional order derivatives for the management and simulation of a fractional order disorderly finance system. In the developed system, we add the critical minimum interest ratedparameter in order to develop a new stable financial model. The new emerging paradigm increases the demand for innovation, which is the gateway to the knowledge economy. The derivatives are characterized in the Caputo fractional order derivative and Atangana-Baleanu derivative. We prove the existence and uniqueness of the solutions with fixed point theorem and an iterative scheme. The interest rate begins to rise according to initial conditions as investment demand and price exponent begin to fall, which shows the financial system's actual macroeconomic behavior. Specifically component of its application to the large scale and smaller scale forms, just as the utilization of specific strategies and instruments such fractal stochastic procedures and expectation.
Citation - WoS: 8
Citation - Scopus: 8
Analysis of HIV/AIDS model with Mittag-Leffler kernel
(Amer inst Mathematical Sciences-aims, 2022) Akram, Muhammad Mannan; Jarad, Fahd; Farman, Muhammad; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Partohaghigh, Mohammad; Jarad, Fahd; 234808; Matematik
Recently different definitions of fractional derivatives are proposed for the development of real-world systems and mathematical models. In this paper, our main concern is to develop and analyze the effective numerical method for fractional order HIV/ AIDS model which is advanced approach for such biological models. With the help of an effective techniques and Sumudu transform, some new results are developed. Fractional order HIV/AIDS model is analyzed. Analysis for proposed model is new which will be helpful to understand the outbreak of HIV/AIDS in a community and will be helpful for future analysis to overcome the effect of HIV/AIDS. Novel numerical procedures are used for graphical results and their discussion.
Citation - WoS: 3
Citation - Scopus: 3
Computational analysis of COVID-19 model outbreak with singular and nonlocal operator
(Amer inst Mathematical Sciences-aims, 2022) Amin, Maryam; Jarad, Fahd; Farman, Muhammad; Akgul, Ali; Partohaghighi, Mohammad; Jarad, Fahd; 234808; Matematik
The SARS-CoV-2 virus pandemic remains a pressing issue with its unpredictable nature, and it spreads worldwide through human interaction. Current research focuses on the investigation and analysis of fractional epidemic models that discuss the temporal dynamics of the SARS-CoV-2 virus in the community. In this work, we choose a fractional-order mathematical model to examine the transmissibility in the community of several symptoms of COVID-19 in the sense of the Caputo operator. Sensitivity analysis of R0 and disease-free local stability of the system are checked. Also, with the assistance of fixed point theory, we demonstrate the existence and uniqueness of the system. In addition, numerically we solve the fractional model and presented some simulation results via actual estimation parameters. Graphically we displayed the effects of numerous model parameters and memory indexes. The numerical outcomes show the reliability, validation, and accuracy of the scheme.
Citation - WoS: 26
Citation - Scopus: 28
Dynamical Transmission of Coronavirus Model with Analysis and Simulation
(Tech Science Press, 2021) Farman, Muhammad; Baleanu, Dumitru; Akgul, Ali; Ahmad, Aqeel; Baleanu, Dumitru; Saleem, Muhammad Umer; 56389; Matematik
COVID-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.
Citation - WoS: 21
Citation - Scopus: 23
Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects
(Tech Science Press, 2021) Farman, Muhammad; Baleanu, Dumitru; Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Naeem, Muhammad; Baleanu, Dumitru; 56389; Matematik
Today, 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.
Citation - WoS: 47
Citation - Scopus: 54
Modelling and Analysis of a Measles Epidemic Model with the Constant Proportional Caputo Operator
(Mdpi, 2023) Farman, Muhammad; Baleanu, Dumitru; Shehzad, Aamir; Akgul, Ali; Baleanu, Dumitru; De la Sen, Manuel; 56389; Matematik
Despite 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.
Citation - WoS: 6
Citation - Scopus: 6
On Solutions of the Stiff Differential Equations in Chemistry Kinetics With Fractal-Fractional Derivatives
(Asme, 2022) Farman, Muhammad; Jarad, Fahd; Aslam, Muhammad; Akgul, Ali; Jarad, Fahd; 234808; Matematik
In 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.