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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 Newton-type technique for solving absolute value equations(Elsevier, 2023) Khan, Alamgir; Iqbal, Javed; Akgul, Ali; Ali, Rashid; Du, Yuting; Hussain, Arafat; Nisar, Kottakkaran SooppyThe Newton-type technique is proposed for solving absolute value equations. This new method is a two-step technique with the generalized Newton technique as a predictor and corrector step is the Simpson's method. Convergence results are established under mild assumptions. The Newton-type technique is very simple and easy to implement. The proposed method is very effective to solve large systems. The heat equation is solved by using the proposed technique. Numerical out-comes show the efficiency of our technique. We add the concluding remarks at the end of this paper. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).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 of respiratory mechanics models with different kernels(De Gruyter Poland Sp Z O O, 2022) Akgul, Esra Karatas; Akgul, Ali; Jamshed, Wasim; Rehman, Zulfiqar; Nisar, Kottakkaran Sooppy; Alqahtani, Mohammed S.; Abbas, MohamedIn this article, we investigate the mechanics of breathing performed by a ventilator with different kernels by an effective integral transform. We mainly obtain the solutions of the fractional respiratory mechanics model. Our goal is to give the underlying model flexibly by making use of the advantages of the non-integer order operators. The big advantage of fractional derivatives is that we can formulate models describing much better the systems with memory effects. Fractional operators with different memories are related to different types of relaxation process of the non-local dynamical systems. Additionally, since we consider the utilisation of different kinds of fractional derivatives, most often having benefit in the implementation, the similarities and differences can be obviously seen between these derivatives.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 Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator(Public Library Science, 2024) Nisar, Kottakkaran Sooppy; Farman, Muhammad; Jamil, Khadija; Akgul, Ali; Jamil, SabaIn this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel'a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton's polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.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 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 HUMAN LIVER MODEL WITH FRACTIONAL OPERATOR(World Scientific Publ Co Pte Ltd, 2023) Azeem, Muhammad; Farman, Muhammad; Abukhaled, Marwan; Nisar, Kottakkaran Sooppy; Akgul, AliThis paper will introduce novel techniques for a fractional-order model of the human liver involving the Atangana-Baleanu, Atangana-Toufik, and the Fractal fractional method with the nonsingular kernel. These techniques give more accurate and appropriate results. Existence and uniqueness have been developed with the help of fixed-point theory results. Numerical simulations are done from the developed algorithm of the model to elaborate the effect of fractional values and justify the theoretical results. Such kind of analysis will be useful for further investigation of epidemic diseases, and also provide a better understanding of disease dynamics to overcome the effect of disease in a community.Öğe Finite difference simulations for magnetically effected swirling flow of Newtonian liquid induced by porous disk with inclusion of thermophoretic particles diffusion(Elsevier, 2022) Bilal, S.; Shah, Imtiaz Ali; Akgul, Ali; Nisar, Kottakkaran Sooppy; Khan, Ilyas; Khashan, M. Motawi; Yahia, I. S.Heat and mass transfer analysis of viscous liquid flow generated by rotation of disk has generated prodigious interest due to promising utilizations in numerous processes such as thermal energy generation systems, turbine rotators, geothermal energy preservations, chemical processing, medicinal instrumentations, computing devices and so forth. In view of such extraordinary utilizations in numerous engineering procedures existent exertion is excogitated to disclose flowing phenomenon over rotating disk. To raise the importance of current analysis influential physical aspects like magnetic field, permeability, Dufour and Soret diffusion phenomenon are also incorporated. Subsequently, flow field distributions are analyzed for suction and injection cases. Modelling is structured via PDE's by obliging constitutive conservation laws. Boundary layer approach is executed to reduce complexity of attained partial differential system. Transformations developed by Karman are implemented to convert developed differential framework into ODE's. Implicitly finite differenced technique known as Keller Box is engaged to find solution of coupled intricate high order ordinary differential equations. Influence of flow controlling parameters on associated distributions are revealed through graphical and tabular representations. The related quantities of engineering interest like coefficients of wall drag force, along radial and tangential directions are also computed. Credibility of presently computed results is established by constructing comparison with previously published literature. It is inferred that magnetic strength parameter enhances tangential and radial components of velocity whereas contrary trend is depicted in axially directed velocity. In addition, temperature and momentum distributions show up surging attribute versus magnetic field parameter. All associated profiles have exhibited decrementing aspects against suction parameter. It is also revealed that increment in Soret tends to produce depreciation in temperature profile whereas concentration distribution is enhanced. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.Öğe Fractional order model for complex Layla and Majnun love story with chaotic behaviour(Elsevier, 2022) Farman, Muhammad; Akgul, Ali; Aldosary, Saud Fahad; Nisar, Kottakkaran Sooppy; Ahmad, AqeelThe main purpose of the present paper is to develop and analyze fractional order dynamical model describing the change in behavior exhibited by a couple in a passionate relationship of love. Model is treated with advanced fractional operators like Atangana-Baleanu Caputo sense, Atanagana-Toufik scheme, and fractal fractional for dynamical behavior of real love story. Its ability is to show constantly changed chaotic behavior of two individuals in the relationship, the model was previously expressed in love triangles. The System is analyzed by using the fixed point theory technique, the existence and uniqueness of system are proved as well as analyzed qualitatively. Also verify the local and global stability of the fractional order system. Numerical simulations are made with the Atanagana-Toufik scheme and fractal fractional operator to measure the emotions and love relationships between two peoples. Advanced approach of such applications opens the path to foresee the love relation after observing the human personality.(c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).Öğe Generalized Ulam-Hyers-Rassias stability and novel sustainable techniques for dynamical analysis of global warming impact on ecosystem(Nature Portfolio, 2023) Farman, Muhammad; Shehzad, Aamir; Nisar, Kottakkaran Sooppy; Hincal, Evren; Akgul, Ali; Hassan, Ahmed MuhammadMarine structure changes as a result of climate change, with potential biological implications for human societies and marine ecosystems. These changes include changes in temperatures, flow, discrimination, nutritional inputs, oxygen availability, and acidification of the ocean. In this study, a fractional-order model is constructed using the Caputo fractional operator, which singular and nol-local kernel. A model examines the effects of accelerating global warming on aquatic ecosystems while taking into account variables that change over time, such as the environment and organisms. The positively invariant area also demonstrates positive, bounded solutions of the model treated. The equilibrium states for the occurrence and extinction of fish populations are derived for a feasible solution of the system. We also used fixed-point theorems to analyze the existence and uniqueness of the model. The generalized Ulam-Hyers-Rassias function is used to analyze the stability of the system. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version for the power law kernel and also compared the results with an exponential law and Mittag Leffler kernel. We also produce graphs of the model at various fractional derivative orders to illustrate the important influence that the fractional order has on the different classes of the model with the memory effects of the fractional operator. To help with the oversight of fisheries, this research builds mathematical connections between the natural world and aquatic ecosystems.Öğe Impact of gold nanoparticles along with Maxwell velocity and Smoluchowski temperature slip boundary conditions on fluid flow: Sutterby model(Elsevier, 2022) Sajid, Tanveer; Jamshed, Wasim; Shahzad, Faisal; Akgul, Esra Karatas; Nisar, Kottakkaran Sooppy; Eid, Mohamed R.Communication is structured to develop a novel three dimensional mathematical model regarding rotating Sutterby fluid flow subjected to a slippery expandable sheet. The heat transfer analysis has been carried out with the inclusion of effects like gold nanoparticles and thermal radiation. The mass transfer regarding the concentration of the fluid has been analysed with the utilization of the activation energy effect. Maxwell velocity and Smoluchowksi temperature slip boundary conditions have been employed. The mathematically modelled partial differential equations (PDEs) regarding momentum, energy, and concentration step down into ordinary differential equations (ODEs) with the utilization of suitable transformation. Matlab built-in bvp4c numerical scheme has been used to handle dimensionless ODEs. The physical quantities like surface drag coefficient, heat transfer as well as mass transfer in the case of variation in various sundry parameters are numerically computed and displayed in the form of tables and figures. The temperature field amplifies by the virtue of augmentation in gold nanoparticles volume fraction and an increment in activation energy booms the mass fraction field. It is observed that the presence of the thermal radiation parameter enhances the heat transfer rate 17.2% and mass transfer booms 62.1% in the case reaction rate constant.Öğe Mathematical study of fractal-fractional leptospirosis disease in human and rodent populations dynamical transmission(Elsevier, 2024) Farman, populations dynamical Muhammad; Jamil, Saba; Nisar, Kottakkaran Sooppy; Akgul, AliIn both industrialized and developing nations, leptospirosis is one of the most underdiagnosed and underreported diseases. It is known that people are more likely to contract a disease depending on their employment habits and the environment they live in, which varies from community to community. The absence of global data for morbidity and mortality has contributed to leptospirosis' neglected disease status even though it is a life -threatening illness and is widely acknowledged as a significant cause of pulmonary hemorrhage syndrome. This study aims to examine the impact of rodent -borne leptospirosis on the human population by constructing and evaluating a compartmental mathematical model using fractional -order differential equations. The model considers both the presence of disease -causing agents in the environment and the rate of human infection resulting from interactions with infected rodents and the environment. Through this approach, the research investigates the dynamics and implications of leptospirosis transmission in the context of human -rodent interactions and environmental factors. We create a fractal -fractional model using the mittag-leffler kernel. The positivity and boundedness of solutions are first discussed. The model equilibria and fundamental reproduction number are then presented. With the use of the Lyapunov function method, the solutions are subjected to global stability analysis. The fixed-point theory is used to derive the fractional -order model's existence and uniqueness. Solutions are produced using a two-step Lagrange polynomial in the generalized form of the Mittag-Leffler kernel to explore the effect of the fractional operator with numerical simulations, which shows the influence of the sickness due to the effect of different parameters involved. Such a study will aid in the development of control strategies to combat the disease in the community and an understanding of the behavior of the Leptospira virus.Öğe Modeling and analysis fractal order cancer model with effects of chemotherapy(Pergamon-Elsevier Science Ltd, 2022) Xu, Changjin; Farman, Muhammad; Akguel, Ali; Nisar, Kottakkaran Sooppy; Ahmad, AqeelIn the study, the sudden act of the cancer model was studied utilizing the fractional operator and its applications to discretize the conformable cancer model. A collection of nonlinear fractional differential equations make up the fractional-order model. We also look at the fractional-order model, which examines how chemotherapeutic attention medications, when combined, interact with the immune system and cancer cells. Both qualitative and quantitative research has been conducted on the cancer model. The proposed fractional-order cancer model's first and second derivatives of Lyapunov stability, positivity, and boundedness are all checked using nonlinear analysis. A generalized Mittag Leffler kernel is used through the ABC derivative, which is also used to check the dynamical behavior of the model. Also, utilizing alternative dimensions of fractional order and validating the effect of fractional parameters, a comparison was made to check the efficiency of the scheme for all compartments. Finally, the physiological results are analyzed and showing off is scooped up to demonstrate cancer disease and corroborate logical findings, which will be useful for future study and reducing cancer's social effect. (c) 2022 Elsevier Ltd. All rights reserved.Öğe Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model(Elsevier, 2021) Hussain, Ghulam; Khan, Tahir; Khan, Amir; Inc, Mustafa; Zaman, Gul; Nisar, Kottakkaran Sooppy; Akgul, AliNovel coronavirus disease is a burning issue all over the world. Spreading of the novel coronavirus having the characteristic of rapid transmission whenever the air molecules or the freely existed virus includes in the surrounding and therefore the spread of virus follows a stochastic process instead of deterministic. We assume a stochastic model to investigate the transmission dynamics of the novel coronavirus. To do this, we formulate the model according to the charectersitics of the corona virus disease and then prove the existence as well as the uniqueness of the global positive solution to show the well posed-ness and feasibility of the problem. Following the theory of dynamical systems as well as by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions of the extinction and the existence of stationary distribution. Finally, we carry out the large scale numerical simulations to demonstrate the verification of our analytical results. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.Öğe Numerical investigation of generalized perturbed Zakharov-Kuznetsov equation of fractional order in dusty plasma(Taylor & Francis Ltd, 2022) Ali, Nasir; Nawaz, Rashid; Zada, Laiq; Nisar, Kottakkaran Sooppy; Ali, Zahid; Jamshed, Wasim; Hussain, Syed M.In the present work, the new iterative method with a combination of the Laplace transform of the Caputo's fractional derivative has been applied to the generalized (3 + 1) dimensional fractional perturbed Zakharov-Kuznetsov equation in a dusty plasma. The proposed method is applied without any discretization and linearization. The numerical and graphical results show the accuracy of the proposed method for nonlinear differential equations. Moreover, the methods are easy to implement and give the efficient approximate solutions.Öğe On solutions of gross domestic product model with different kernels(Elsevier, 2022) Akgul, Esra Karatas; Jamshed, Wasim; Nisar, Kottakkaran Sooppy; Elagan, S. K.; Alshehri, Nawal A.In this paper, we investigate gross domestic product model with four different fractional derivatives. We find the solutions of fractional models by utilizing Sumudu transform. We prove the efficiency of the Sumudu transform by some theoretic outcomes and applications. We demonstrate the simulations by some figures. We show the agreement of different fractional derivatives on the model. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.Öğe Onset about non-isothermal flow of Williamson liquid over exponential surface by computing numerical simulation in perspective of Cattaneo Christov heat flux theory(Elsevier, 2022) Bilal, S.; Shah, M. Imtiaz; Khan, Noor Zeb; Akgul, Ali; Nisar, Kottakkaran SooppyIn view of increaing significance of non-isothermal flow of non-Newtonian fluids over exponential surfaces in numerous industrial and technological procedures such as film condensation, extrusion of plastic sheets, crystal growth, cooling process of metallic sheets, design of chemical processing equipment and various heat exchangers, and glass and polymer industries current disquisition is addressed. For comprehensive examination Williamson model expressing the attributes of shear thickening and thinning liquids is taken under consideration. The physical aspects of magnetic field applied in transverse direction to flow is also accounted. Heat transfer aspects are incorporated and analyzed by employing Cattaneo-Christov heat flux model. Mathematical formulation of problem is conceded in the form of PDE's by implementing boudary layer approach and later on converted into ODE's with the assistance of transformation procedure. The resulting equations are solved numerically using shooting and Runge-Kutta methods. Impact of involved parameters on flow distributions is displayed through graphs. From the analysis it is inferred that Cattaneo Christov heat flux law exhibits hyperbolic equation which follows the causality principle and make the problem more compatible to real world applications. It is also deduced that magnetic field suppresses the velocity field and associated boundary layer region. Decrease in temperature profile and heat transfer coefficient is found against inciting magnitude of thermal relaxation parameter. Substantial decrease in velocity is found against increasing magnitude of Williamson fluid parameter and magnetic field parameter whereas skin friction coefficient increments. Confir-mation about present findings is executed by making comparison with existing literature.(c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Öğe Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator(Nature Portfolio, 2024) Jamil, Saba; Bariq, Abdul; Farman, Muhammad; Nisar, Kottakkaran Sooppy; Akguel, Ali; Saleem, Muhammad UmerRespiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam-Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power-Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.
