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Öğe A mathematical analysis and simulation for Zika virus model with time fractional derivative(Wiley, 2020) Farman, Muhammad; Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Rizwan, Muhammad; Ahmad, Muhammad OzairZika is a flavivirus that is transmitted to humans either through the bites of infected Aedes mosquitoes or through sexual transmission. Zika has been associated with congenital anomalies, like microcephalus. We developed and analyzed the fractional-order Zika virus model in this paper, considering the vector transmission route with human influence. The model consists of four compartments: susceptible individuals arex(1)(t), infected individuals arex(2)(t),x(3)(t)shows susceptible mosquitos, andx(4)(t)shows the infected mosquitos. The fractional parameter is used to develop the system of complex nonlinear differential equations by using Caputo and Atangana-Baleanu derivative. The stability analysis as well as qualitative analysis of the fractional-order model has been made and verify the non-negative unique solution. Finally, numerical simulations of the model with Caputo and Atangana Baleanu are discussed to present the graphical results for different fractional-order values as well as for the classical model. A comparison has been made to check the accuracy and effectiveness of the developed technique for our obtained results. This investigative research leads to the latest information sector included in the evolution of the Zika virus with the application of fractional analysis in population dynamics.Öğe Analysis and controllability of diabetes model for experimental data by using fractional operator(Elsevier, 2024) Farman, Muhammad; Ahmad, Aqeel; Zehra, Anum; Nisar, Kottakkaran Sooppy; Hincal, Evren; Akgul, AliDiabetes is a silent illness that is endangering public health in society. Diabetes is a chronic disease affecting millions of people worldwide, and understanding the underlying mechanisms of glucose homeostasis is crucial for managing this condition. Diabetes is a significant public health issue due to the early morbidity, mortality, shortened life expectancy, and financial and other expenses to the patient, their careers, and the health care system. In this study, we propose a mathematical model consisting of fl-cells, insulin, glucose, and growth hormone that incorporates the fractional operator. Using the Lyapunov function, we treated a global stability analysis and investigated the impact of a new wave of dynamical transmission on the equilibrium points of the second derivative. With the Lipschitz criteria and linear growth, the exact singular solution for the proposed model has been determined. Furthermore, we present a detailed analysis of infections, and numerical simulations are conducted using the Mittag-Leffler Kernel mathematical framework to illustrate the theoretical conclusions for various orders of the fractional derivative. Controllability and observability of the linear system are treated for close loop design to check the relation between the glucose and insulin systems. Overall, our results provide a comprehensive understanding of glucose homeostasis and its underlying mechanisms, contributing to the development of effective diabetes management strategies. The proposed model and mathematical framework offer a valuable tool for investigating complex systems and phenomena, with applications beyond the field of diabetes research and helpful to designing the closed loop for the glucose-insulin system.Öğe Analysis and dynamical behavior of fractional-order cancer model with vaccine strategy(Wiley, 2020) Farman, Muhammad; Akgul, Ali; Ahmad, Aqeel; Imtiaz, SumiyahIn recent year, the world has witnessed the arrival of deadly diseases like cancer over all the global levels. To fight back this disease or control the spread, mankind relies on modeling and medicine to control, cure, and behavior of the cancer diseases. We developed the fractional-order immunotherapy bladder cancer model and used the BCG vaccine for treatment by using the Caputo fractional derivative operator phi e(0,1]. A mathematical model has four variables B,E, T-i, T-u which represent the vaccine for the immune system, effector cells, total population of affected, and unaffected cells, respectively. In this model, we have two cases according to the growth rate of cells. The fractional-order system is stable in both cases and gives the solution infeasible region for uniqueness, positivity, and boundedness to illustrate the treatment of cancer. The effect of fractional parameter on our obtained solutions is presented, and a comparison is made with the classical ordinary derivative operator. It is worthy to observe that fractional derivatives show significant changes and memory effects as compared with ordinary derivatives to control the disease at the initial stage to overcome the risk of living with cancer.Öğe Analysis and Modeling of Fractional Order Model for Hepatitis B at Different Stages(Natural Sciences Publishing, 2023) Raza, Ali; Farman, Muhammad; Ahmad, Aqeel; Akgul, Ali; Sultan, Muhammad; Al Bayatti, HilalFractional operator is used to construct the framework of complex hepatitis B by using Caputo and Caputo Fabrizio fractional order derivative. Examination the uniqueness and stability to test the viability of the fractional order model with the proposed numerical plan as well as analyzes qualitatively. Union of different parts behind iterative approach on account of Fabrizio offers a bounded solution that accomplished required outcomes. The fractional system of differential equations which has four parts, susceptible individuals A(t), acute infected B(t),C(t) is chronic hepatitis and I(t) represents individuals who have retrieve after the infection with a life time freedom. At the end, the impact of the framework parameter on the spread of the ailment are begun to analyze using the numerical simulations. © 2023 NSP Natural Sciences Publishing Cor.Öğe Analysis and Modeling of HIV Dynamical Transmission(Natural Sciences Publishing, 2022) Farman, Muhammad; Zafar, Nayab; Akgul, Ali; Kouser, Farhina; Tabassum, Muhammad Farhan; Ahmad, Aqeel; Ahmad, Muhammad O.In this article, HIV fractional order model is analyzed to reduce its effect on community and for control strategy. Verify the unique solutions of the proposed system as well as proved the stability analysis. Fractional order system is solved by using the Caputo fractional derivative operator b 2 (0,1] to check the effect of fractional parameter. Simulations are made to check the actual behavior of the HIV disease in the society. Such kind of analysis help to understand the outbreak of HIV and for future control strategy. © 2022 NSPÖğe Analysis and Modelling of HIV/AIDS Model with Fractional Order Parameter Estimation(Natural Sciences Publishing, 2022) Farman, Muhammad; Raza, Ali; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Iqbal, Muhammad SajidIn this paper, nonlinear fractional order HIV/AIDS mathematical model is discussed epidemic problems for the complex transmission of the disease. It is accepted that susceptible wind up contaminated by means of sexual contacts with infective eventually create AIDS. The point of this task was to amend transmission models recently created to represent HIV transmission and AIDS related mortality. The Caputo-Fabrizio fractional derivative operator of order ? ? (0,1) is used to obtain fractional differential equations structure. The stability fractional order model was developed and the unique non-negative solution was tested. The numerical simulations are performed using an iterative technique. Some new results are being viewed with the help of Sumudo transform. Nonetheless, according to Banach, the related findings are given nonlinear functional analysis and fixed point theory. However, mathematical simulations are also acknowledged to evaluate the impact of the model’s parameter by decreasing the fractional values and showing the effect of the b fractional parameter on our obtained solutions. The impact of various parameters is represented graphically. © 2022. NSP Natural Sciences Publishing Cor.Öğe Analysis and simulation of fractional-order diabetes model(Erdal Karapinar, 2020) Ahmad, Aqeel; Farman, Muhammad; Akgül, AliIn this article, we research the diabetes model and its consequences using the Caputo and Atangana Baleanu fractional derivatives. A deterministic mathematical model is corresponding to the fractional derivative of diabetes mellitus. The Laplace transformation is used for the diagnostic structure of the diabetes model. Picard-Lindelof 's method shows the existence and uniqueness of the solution. Finally, numerical simulations are made to illustrate the effects of changing the fractional-order to obtain the theoretical results, and comparisons are made for the Caputo and Atangana Baleanu derivative. The results of the following work by controlling plasma glucose with the fractional-order model make it a suitable candidate for controlling human type 1 diabetes. © 2020, Erdal Karapinar. All rights reserved.Öğe Analysis of Fractional Order Chaotic Financial Model with Minimum Interest Rate Impact(Mdpi, 2020) Farman, Muhammad; Akgul, Ali; Baleanu, Dumitru; Imtiaz, Sumaiyah; Ahmad, AqeelThe 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.Öğe Analysis of HIV/AIDS model with Mittag-Leffler kernel(Amer Inst Mathematical Sciences-Aims, 2022) Akram, Muhammad Mannan; Farman, Muhammad; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Partohaghigh, Mohammad; Jarad, FahdRecently 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.Öğe Bacillus Calmette Guerin (BCG) Immunotherapy for Bladder Cancer: A Control and Mathematical Analysis(Springer, 2021) Akgül, Ali; Farman, Muhammad; Ahmad, Aqeel; Saleem, Muhammad UmerIn this manuscript, Immunotherapy with Bacillus Calmette Guerin (BCG) vaccine is devised for treating spherical bladder cancer. We considered the cancer model regarding tumor-immune connections in the bladder as a result of BCG therapy and check the input and output of the system. Controllability and observability are treated for the logistic model and exponential model for cancer according to parameter values. Consider the system for stability investigation about the point of equilibrium and taking Bacillus Calmette Guerin (BCG) vaccine concentration as an input and effector cells are output in the system under consideration. The model clarifies that the concentration of immunotherapy should be held in prescribed limits. Also, numerical simulations are carried of the proposed techniques to show the actual behavior of the system to support the biological results. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.Öğe Close Loop Design in Glucose Insulin Model with Effect of Physical Exercise(Shahid Chamran Univ Ahvaz, Iran, 2021) Farman, Muhammad; Akgul, Ali; Ahmad, AqeelThe minimal mathematical models for exercise and its extension is included the major exercise effects on plasma glucose and insulin levels. Model expectations for glucose and insulin dynamics are steady with current literature statistics. The extended model offers innovative disruption test stage for the enlargement of closed-loop glucose control algorithms. Stability analysis as well as qualitative analysis has been made for the model. We treat the controllability and observability of the system for glucose insulin regulatory system during feedback design. Numerical simulation has been carried out to check the effectiveness and actual behavior for the proposed system.Öğe Computational analysis of corruption dynamics insight into fractional structures(Taylor & Francis Ltd, 2024) Akgul, Ali; Farman, Muhammad; Sutan, Muhammad; Ahmad, Aqeel; Ahmad, Sheraz; Munir, Arshad; Hassani, Murad KhanThe fractional derivative that is used to compute the solution of the corruption system with Power-Law Kernel, Mittag-Leffler Kernel, and Exponential Decay Kernel. It is important to study and analyse corruption dynamics, because it is an act that has a direct effect on public rights, and because of this the right of the rightful owner, just got destroyed. Using hypothesis theory for differential equation, this work suggests and assesses a nonlinear deterministic model for the dynamics of corruption. Positivity and boundedness are verified for the proposed corruption model to identify the level of resolution of corruption factor in society. Fractional-order corruption model is investigated with different kernels for efficient results. The necessary criteria for the best control of corruption transmission were identified using Pontryagin's maximal concept. The numerical simulation showed that corruption must be resisted by an integrated control strategy. Numerical simulations are used to demonstrate the correctness of the proposed approaches. Finally, simulations are derived for the proposed schemes to check the effectiveness of the results and to analyse the corruption behaviour in society as well as dynamically highlight the propagation of corruption group.Öğe Computer Virus Fractional Order Model with Effects of Internal and External Storage Media(New York Business Global Llc, 2022) Farman, Muhammad; Akgul, Ali; Shanak, H.; Asad, Jihad; Ahmad, AqeelIn this work, we focus on the implementation of epidemic techniques on computer virus and study the dynamic transmission of several viruses to minimize the destruction of computers. We aim to make and analyze computer viruses through the Atangana-Baleanu sense and the Atangana-Taufik scheme, which is used for the fractional derivative model for the computer virus epidemic. It contained infected external computer effects and removable storage media on the computer viruses. For the validation of the model, we also discussed its positivity and boundedness. Fixed point theory and the iterative methods helped a lot to find out the existence and uniqueness of the model. In the case of numerical simulation, we used Atanagana-Taufik technique to illustrate the effects of varying the fractional order. The graphical results support our theoretical results from which, we analyze the infected external computer effects and removable storage media on the computer viruses.Öğe Dynamical Behavior andMathematical Analysis of Fractional Order Smoking Model(L and H Scientific Publishing, LLC, 2023) Ahmad, Aqeel; Farman, Muhammad; Akgul, Ali; Khan, AdnanIn this paper the fractional order smoking model is represent with Caputo and Caputo Fabrizio fractional derivative operator of order ? ? (0,1] for dynamical transmission of smoking. Human beings face dangerous diseases caused by smoking, including arms, lungs, stomach, cervix, breast, pancreatic cancer and many others. Stability and qualitative analysis of model is studied to show the dynamical behaviour of the model in feasible region. It’s important to note that a more powerful approach for computing convergent solutions is applied for mathematical models based on a fractional order differential equation structure. Study of the convergence is often provided to demonstrate the process’s effectiveness. It shows the stability, uniqueness and applicability of the model for the control of smoking in the society. Numerical simulation are established to show the actual behavior of the smoking spread. © 2023 L&H Scientific Publishing, LLC. All rights reserved.Öğe Dynamical behavior of tumor-immune system with fractal-fractional operator(Amer Inst Mathematical Sciences-Aims, 2022) Farman, Muhammad; Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Nisar, Kottakkaran Sooppy; Vijayakumar, VelusamyIn this paper, the dynamical behavior of the fractional-order cancer model has been analyzed with the fractal-fractional operator, which discretized the conformable cancer model. The fractional-order model consists of the system of nonlinear fractional differential equations. Also, we discuss the fractional-order model to check the relationship between the immune system and cancer cells by mixing IL-12 cytokine and anti-PD-L1 inhibitor. The tumor-immune model has been studied qualitatively as well as quantitatively via Atangana-Baleanu fractal-fractional operator. The nonlinear analysis is used to check the Ulam-Hyres stability of the proposed model. Moreover, the dynamical behavior for the fractional-order model has been checked by using a fractal-fractional operator with a generalized Mittag-Leffler Kernel and verifying the effect of fractional parameters. Finally, the obtained solutions are interpreted biologically, and simulations are carried out to illustrate cancer disease and support theoretical results, which will be helpful for further analysis and to control the effect of cancer in the community.Öğe Dynamical behaviour of fractional-order finance system(Indian Acad Sciences, 2020) Farman, Muhammad; Akguel, Ali; Saleem, Muhammad Umer; Imtiaz, Sumaiyah; Ahmad, AqeelIn this paper, we developed the fractional-order finance system transmission model. The main objective of this paper is to construct and evaluate a fractional derivative to track the shape of the dynamic chaotic financial system of fractional order. The numerical solution for fractional-order financial system is determined using the Atangana-Baleanu-Caputo (ABC) and Caputo derivatives. Picard-Lindelof's method shows the existence and uniqueness of the solution. Numerical techniques show that ABC derivative strategy can be used effectively to overcome the risk of investment. An active control strategy for controlling chaos is used in this system. The stabilisation of equilibrium is obtained by both theoretical analysis and simulation results.Öğe Dynamical Transmission of Coronavirus Model with Analysis and Simulation(Tech Science Press, 2021) Farman, Muhammad; Akgul, Ali; Ahmad, Aqeel; Baleanu, Dumitru; Saleem, Muhammad UmerCOVID-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.Öğe Epidemiological analysis of fractional order COVID-19 model with Mittag-Leffler kernel(Amer Inst Mathematical Sciences-Aims, 2022) Farman, Muhammad; Akgul, Ali; Nisar, Kottakkaran Sooppy; Ahmad, Dilshad; Ahmad, Aqeel; Kamangar, Sarfaraz; Saleel, C. AhamedThis paper derived fractional derivatives with Atangana-Baleanu, Atangana-Toufik scheme and fractal fractional Atangana-Baleanu sense for the COVID-19 model. These are advanced techniques that provide effective results to analyze the COVID-19 outbreak. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model COVID-19 model. We also proved the property of boundedness and positivity for the fractional-order model. The Atangana-Baleanu technique and Fractal fractional operator are used with the Sumudu transform to find reliable results for fractional order COVID-19 Model. The generalized Mittag-Leffler law is also used to construct the solution with the different fractional operators. Numerical simulations are performed for the developed scheme in the range of fractional order values to explain the effects of COVID-19 at different fractional values and justify the theoretical outcomes, which will be helpful to understand the outbreak of COVID-19 and for control strategies.Öğe Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects(Tech Science Press, 2021) Farman, Muhammad; Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Naeem, Muhammad; Baleanu, DumitruToday, 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.Öğe Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures(Nature Portfolio, 2024) Ahmad, Aqeel; Abbas, Fakher; Farman, Muhammad; Hincal, Evren; Ghaffar, Abdul; Akgul, Ali; Hassani, Murad KhanTo study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model. A newly developed system SEIBR, which is examined both qualitatively and quantitatively to determine its stable position as well as the verification of flip bifurcation has been made for developed system. The local stability of this model has been explored concerning limited observations, a fundamental aspect of epidemic models. We have derived the reproductive number using next generation method, denoted as R 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}$$\end{document} , to analyze its impact rate across various sub-compartments, which serves as a critical determinant of its community-wide transmission rate. The sensitivity analysis has been verified according to its each parameters to identify that how much rate of change of parameters are sensitive. Atangana-Toufik scheme is employed to find the solution for the developed system using different fractional values which is advanced tool for reliable bounded solution. Also the error analysis has been made for developed scheme. Simulations have been made to see the real behavior and effects of cholera disease with early detection and treatment by implementing remedial methods without the use of drugs in the community. Also identify the real situation the spread of cholera disease after implementing remedial methods with and without the use of drugs. Such type of investigation will be useful to investigate the spread of virus as well as helpful in developing control strategies from our justified outcomes.
