Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 14Citation - Scopus: 16Analysis of the Fractional Diarrhea Model With Mittag-Leffler Kernel(Amer inst Mathematical Sciences-aims, 2022) Iqbal, Muhammad Sajid; Ahmed, Nauman; Akgul, Ali; Raza, Ali; Shahzad, Muhammad; Iqbal, Zafar; Jarad, FahdIn this article, we have introduced the diarrhea disease dynamics in a varying population. For this purpose, a classical model of the viral disease is converted into the fractional-order model by using Atangana-Baleanu fractional-order derivatives in the Caputo sense. The existence and uniqueness of the solutions are investigated by using the contraction mapping principle. Two types of equilibrium points i.e., disease-free and endemic equilibrium are also worked out. The important parameters and the basic reproduction number are also described. Some standard results are established to prove that the disease-free equilibrium state is locally and globally asymptotically stable for the underlying continuous system. It is also shown that the system is locally asymptotically stable at the endemic equilibrium point. The current model is solved by the Mittag-Leffler kernel. The study is closed with constraints on the basic reproduction number R-0 and some concluding remarks.Article Citation - WoS: 47Citation - Scopus: 48Oscillatory and Complex Behaviour of Caputo-Fabrizio Fractional Order Hiv-1 Infection Model(Amer inst Mathematical Sciences-aims, 2022) Ullah, Aman; Partohaghighi, Mohammad; Saifullah, Sayed; Akgul, Ali; Jarad, Fahd; Ahmad, ShabirHIV-1 infection is a dangerous diseases like Cancer, AIDS, etc. Many mathematical models have been introduced in the literature, which are investigated with different approaches. In this article, we generalize the HIV-1 model through nonsingular fractional operator. The non-integer mathematical model of HIV-1 infection under the Caputo-Fabrizio derivative is presented in this paper. The concept of Picard-Lindelof and fixed-point theory are used to address the existence of a unique solution to the HIV-1 model under the suggested operator. Also, the stability of the suggested model is proved through the Picard iteration and fixed point theory approach. The model's approximate solution is constructed through three steps Adams-Bashforth numerical method. Numerical simulations are provided for different values of fractional-order to study the complex dynamics of the model. Lastly, we provide the oscillatory and chaotic behavior of the proposed model for various fractional orders.Article Citation - WoS: 7Citation - Scopus: 6New Solutions of Nonlinear Dispersive Equation in Higher-Dimensional Space With Three Types of Local Derivatives(Mdpi, 2022) Hashemi, Mir Sajjad; Jarad, Fahd; Akgul, AliThe aim of this paper is to use the Nucci's reduction method to obtain some novel exact solutions to the s-dimensional generalized nonlinear dispersive mK(m,n) equation. To the best of the authors' knowledge, this paper is the first work on the study of differential equations with local derivatives using the reduction technique. This higher-dimensional equation is considered with three types of local derivatives in the temporal sense. Different types of exact solutions in five cases are reported. Furthermore, with the help of the Maple package, the solutions found in this study are verified. Finally, several interesting 3D, 2D and density plots are demonstrated to visualize the nonlinear wave structures more efficiently.Article Citation - WoS: 5Citation - Scopus: 7New Applications Related To Hepatitis C Model(Amer inst Mathematical Sciences-aims, 2022) Raza, Ali; Akgul, Ali; Iqbal, Zafar; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Jarad, Fahd; Ahmed, NaumanThe main idea of this study is to examine the dynamics of the viral disease, hepatitis C. To this end, the steady states of the hepatitis C virus model are described to investigate the local as well as global stability. It is proved by the standard results that the virus-free equilibrium state is locally asymptotically stable if the value of R-0 is taken less than unity. Similarly, the virus existing state is locally asymptotically stable if R-0 is chosen greater than unity. The Routh-Hurwitz criterion is applied to prove the local stability of the system. Further, the disease-free equilibrium state is globally asymptotically stable if R-0 < 1. The viral disease model is studied after reshaping the integer-order hepatitis C model into the fractal-fractional epidemic illustration. The proposed numerical method attains the fixed points of the model. This fact is described by the simulated graphs. In the end, the conclusion of the manuscript is furnished.Article Citation - WoS: 1Citation - Scopus: 1Structure Preserving Numerical Analysis of Reaction-Diffusion Models(Wiley, 2022) Rehman, Muhammad Aziz-ur; Adel, Waleed; Jarad, Fahd; Ali, Mubasher; Rafiq, Muhammad; Akgul, Ali; Ahmed, NaumanIn this paper, we examine two structure preserving numerical finite difference methods for solving the various reaction-diffusion models in one dimension, appearing in chemistry and biology. These are the finite difference methods in splitting environment, namely, operator splitting nonstandard finite difference (OS-NSFD) methods that effectively deal with nonlinearity in the models and computationally efficient. Positivity of both the proposed splitting methods is proved mathematically and verified with the simulations. A comparison is made between proposed OS-NSFD methods and well-known classical operator splitting finite difference (OS-FD) methods, which demonstrates the advantages of proposed methods. Furthermore, we applied proposed NSFD splitting methods on several numerical examples to validate all the attributes of the proposed numerical designs.Article Citation - WoS: 20Citation - Scopus: 21Fractional Order Mathematical Model of Serial Killing With Different Choices of Control Strategy(Mdpi, 2022) Ahmad, Shabir; Arfan, Muhammad; Akgul, Ali; Jarad, Fahd; Rahman, Mati UrThe current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag-Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam's stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams-Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.Article Citation - WoS: 1Citation - Scopus: 1Finite Difference Method for Transmission Dynamics of Contagious Bovine Pleuropneumonia(Amer inst Mathematical Sciences-aims, 2022) Modanli, Mahmut; Akgul, Ali; Jarad, Fahd; Kikpinar, SaitIn this study, the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by finite difference method are presented. This model is made up of sensitive, exposed, vaccinated, infectious, constantly infected, and treated compartments. The model is studied by the finite difference method. Firstly, the finite difference scheme is constructed. Then the stability estimates are proved for this model. As a result, several simulations are given for this model on the verge of antibiotic therapy. From these figures, the supposition that 50% of infectious cattle take antibiotic therapy or the date of infection decrease to 28 days, 50% of susceptible obtain vaccination within 73 days.Article Citation - WoS: 18Citation - Scopus: 19Construction and Numerical Analysis of a Fuzzy Non-Standard Computational Method for the Solution of an Seiqr Model of Covid-19 Dynamics(Amer inst Mathematical Sciences-aims, 2022) Ahmed, Nauman; Rafiq, Muhammad; Akgul, Ali; Raza, Ali; Ahmad, Muhammad Ozair; Jarad, Fahd; Dayan, FazalThis current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.Article Citation - WoS: 3Citation - Scopus: 3Computational Analysis of Covid-19 Model Outbreak With Singular and Nonlocal Operator(Amer inst Mathematical Sciences-aims, 2022) Farman, Muhammad; Akgul, Ali; Partohaghighi, Mohammad; Jarad, Fahd; Amin, MaryamThe 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.Article Citation - WoS: 9Citation - Scopus: 9Analysis of Hiv/Aids Model With Mittag-Leffler Kernel(Amer inst Mathematical Sciences-aims, 2022) Farman, Muhammad; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Partohaghigh, Mohammad; Jarad, Fahd; Akram, Muhammad MannanRecently 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.