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Öğe A fractal-fractional sex structured syphilis model with three stages of infection and loss of immunity with analysis and modeling(Elsevier, 2023) Farman, Muhammad; Shehzad, Aamir; Akgul, Ali; Hincal, Evren; Baleanu, Dumitru; El Din, Sayed M.Treponema pallidum, a spiral-shaped bacterium, is responsible for the sexually transmitted disease syphilis. Millions of people in less developed countries are getting the disease despite the accessibility of effective preventative methods like condom use and effective and affordable treatment choices. The disease can be fatal if the patient does not have access to adequate treatment. Prevalence has hovered between endemic levels in industrialized countries for decades and is currently rising. Using the Mittag-Leffler kernel, we develop a fractal-fractional model for the syphilis disease. Qualitative as well as quantitative analysis of the fractional order system are performed. Also, fixed point theory and the Lipschitz condition are used to fulfill the criteria for the existence and uniqueness of the exact solution. We illustrate the system's Ulam-Hyers stability for disease-free and endemic equilibrium. The analytical solution is supported by numerical simulations that show how the dynamics of the spread of syphilis within the population are influenced by fractional-order derivatives. The outcomes show that the suggested methods are effective in delivering better results. Overall, this research helps to develop more precise and comprehensive approaches to understanding and regulating syphilis disease transmission and progression.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 A mathematical fractal-fractional model to control tuberculosis prevalence with sensitivity, stability, and simulation under feasible circumstances(Elsevier Ltd, 2024) Farman, Muhammad; Shehzad, Aamir; Nisar, Kottakkaran Sooppy; Hincal, Evren; Akgul, AliBackground: Tuberculosis, a global health concern, was anticipated to grow to 10.6 million new cases by 2021, with an increase in multidrug-resistant tuberculosis. Despite 1.6 million deaths in 2021, present treatments save millions of lives, and tuberculosis may overtake COVID-19 as the greatest cause of mortality. This study provides a six-compartmental deterministic model that employs a fractal–fractional operator with a power law kernel to investigate the impact of vaccination on tuberculosis dynamics in a population. Methods: Some important characteristics, such as vaccination and infection rate, are considered. We first show that the suggested model has positive bounded solutions and a positive invariant area. We evaluate the equation for the most important threshold parameter, the basic reproduction number, and investigate the model's equilibria. We perform sensitivity analysis to determine the elements that influence tuberculosis dynamics. Fixed-point concepts show the presence and uniqueness of a solution to the suggested model. We use the two-step Newton polynomial technique to investigate the effect of the fractional operator on the generalized form of the power law kernel. Results: The stability analysis of the fractal–fractional model has been confirmed for both Ulam–Hyers and generalized Ulam–Hyers types. Numerical simulations show the effects of different fractional order values on tuberculosis infection dynamics in society. According to numerical simulations, limiting contact with infected patients and enhancing vaccine efficacy can help reduce the tuberculosis burden. The fractal–fractional operator produces better results than the ordinary integer order in the sense of memory effect at diffract fractal and fractional order values. Conclusion: According to our findings, fractional modeling offers important insights into the dynamic behavior of tuberculosis disease, facilitating a more thorough comprehension of their epidemiology and possible means of control. © 2024Öğe A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bio-convection effect(Elsevier B.V., 2023) Ahmad, Bilal; Ozair Ahmad, Muhammad; Farman, Muhammad; Akgül, Ali; Riaz, Muhammad BilalThe aim of this research is to discuss the significance of slip conditions for magnetized nanofluid flow with the impact of nonlinear thermal radiations, activation energy, inclined MHD, sorrot and dufour, and gyrotactic micro motile organisms over continuous stretching of a two-dimensional sheet. The governing equations emerge in the form of partial differential equations. Since the resultant governing differential equations are nonlinear, the partial differential equations are transformed into ordinary differential equations using a workable similarity transformation. By using the Bvp4c module of the MATLAB program, the simplified mathematical framework can be numerically solved. The computation of Coefficients of skin friction, Nusselt numbers, different patterns of velocity profiles, fluid temperature, and concentration profiles reveals the physical nature of this study. As compared to earlier investigations, it was found that the obtained results demonstrated high degrees of symmetry and precision. A decline observes in velocity for boosted values of MHD, inclination, and rotatory parameter. However thermal transportation increases by increasing brownien motion, thermophoresis, radiation and Sorrot effect. The study has significant application in heat control systems, food factories, thermal exchangers, biomechanics, biomedical engineering, and aero dynamical systems © 2022Öğe 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 dynamical transmission of tuberculosis model with treatment effect by using fractional operator(Taylor & Francis Inc, 2024) Farman, Muhammad; Mehmood Malik, Shahid; Akguel, Ali; Ghaffari, Abdul Sattar; Salamat, NadeemEach year, millions of people die from the airborne infectious illness tuberculosis (TB). Several drug-susceptible (DS) and drug-resistant (DR) forms of the causative agent, Mycobacterium tuberculosis (MTB), are currently common in the majority of affluent and developing nations, particularly in Bangladesh, and completely drug-resistant strains are beginning to arise. The main purpose of this research is to develop and examine a non-integer-order mathematical model for the dynamics of tuberculosis transmission using the fractal fractional operator. By demonstrating characteristics such as the boundedness of solutions, positivity, and reliance of the solution on the original data, the biological well-posedness of the mathematical model formulation was investigated for TB cases from 2002 to 2017 in KPK Pakistan. Ulam-Hyres stability is also used to assess both local and global aspects of TB bacterial infection. Sensitivity analysis of the TB model with therapy was also examined. The advanced numerical technique is used to find the solution of the fractional-order system to check the impact of fractional parameters. Simulation highlights that all classes have converging qualities and retain established positions with time, which shows the actual behavior of bacterial infection with TB.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 a fractional order Bovine Brucellosis disease model with discrete generalized Mittag-Leffler kernels(Elsevier, 2023) Farman, Muhammad; Shehzad, Aamir; Akgul, Ali; Baleanu, Dumitru; Attia, Nourhane; Hassan, Ahmed M.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.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 Fractional Order Computer VirusModel with MultipleWays of Infections Potential(L and H Scientific Publishing, LLC, 2023) Akgül, Ali; Farman, Muhammad; Akram, Muhammad Mannan; Sajjad, Assad; Azeem, MuhammadIn this paper, we propose a novel technique for the computer virus epidemic which contains infected external computer effects and removable storage media on the computer viruses. The positivity and boundedness for validation of the model are also discussed. The existence and uniqueness of the system of solutions for the model are made by using fixed point theory and iterative method. Numerical simulation obtained with proposed scheme which shows the impacts of varying the fraction-al-order parameters and the support of the theoretical results. © 2023 L&H Scientific Publishing, LLC. All rights reserved.Öğe ANALYSIS OF FRACTIONAL ORDER DIARRHEA MODEL USING FRACTAL FRACTIONAL OPERATOR(World Scientific Publ Co Pte Ltd, 2022) Yao, Shao-Wen; Ahniad, Aqui; Inc, Mustafa; Farman, Muhammad; Ghaffar, Abdul; Akgul, AliIn this paper, we construct a scheme of fractional-order mathematical model for the population infected by diarrhea disease by using the four compartments S, I, T and R. The fractal-fractional derivative operator (FFO) with generalized Mittag-Leffler kernel is employed to obtain the solution of the proposed system. The system is analyzed qualitatively as well as verify non-negative unique solution. The existence and uniqueness results of fractional-order model under Atangana-Baleanu fractal-fractional operator have been proved by fixed point theory. Also error analysis has been made for the proposed fractional-order model. Simulation has been carried out for derived fractional-order scheme to check the effectiveness of the results which will help, how to prevent and control such type of epidemic in society.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 Analytical study of a Hepatitis B epidemic model using a discrete generalized nonsingular kernel(Amer Inst Mathematical Sciences-Aims, 2024) Farman, Muhammad; Akgul, Ali; Conejero, J. Alberto; Shehzad, Aamir; Nisar, Kottakkaran Sooppy; Baleanu, DumitruHepatitis B is a worldwide viral infection that causes cirrhosis, hepatocellular cancer, the need for liver transplantation, and death. This work proposed a mathematical representation of Hepatitis B Virus (HBV) transmission traits emphasizing the significance of applied mathematics in comprehending how the disease spreads. The work used an updated Atangana-Baleanu fractional difference operator to create a fractional -order model of HBV. The qualitative assessment and wellposedness of the mathematical framework were looked at, and the global stability of equilibrium states as measured by the Volterra -type Lyapunov function was summarized. The exact answer was guaranteed to be unique using the Lipschitz condition. Additionally, there were various analyses of this new type of operator to support the operator's efficacy. We observe that the explored discrete fractional operators will be x 2 -increasing or decreasing in certain domains of the time scale N j : = j , j + 1 ,... by looking at the fundamental characteristics of the proposed discrete fractional operators along with x -monotonicity descriptions. For numerical simulations, solutions were constructed in the discrete generalized form of the Mittag-Leffler kernel, highlighting the impacts of the illness caused by numerous causes. The order of the fractional derivative had a significant influence on the dynamical process utilized to construct the HBV model. Researchers and policymakers can benefit from the suggested model's ability to forecast infectious diseases such as HBV and take preventive action.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.
