Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Department: search.filters.department.Çankaya UniversitySubject: search.filters.subject.Caputo Operator

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Now showing 1 - 10 of 21
  • Article
    A Novel Fractional Case Study of Nonlinear Dynamics Via Analytical Approach
    (Zhejiang Univ Press, 2024) Khan, Hassan; Khan, Adnan; Shah, Rasool; Baleanu, Dumitru
    The present work describes the fractional view analysis of Newell-Whitehead-Segal equations, using an innovative technique. The work is carried with the help of the Caputo operator of fractional derivative. The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method. The derived results are very consistent with the actual solutions to the problems. A graphical representation has been done for the solution of the problems at various fractional-order derivatives. Moreover, the solution in series form has the desired rate of convergence and provides the closed-form solutions. It is noted that the procedure can be modified in other directions for fractional order problems.
  • Article
    Citation - WoS: 43
    Citation - Scopus: 37
    On Fractional-Order Symmetric Oscillator With Offset-Boosting Control
    (Vilnius Univ, inst Mathematics & informatics, 2022) Xu, Changjin; Rahman, Mati ur; Baleanu, Dumitru
    This article analyzes the dynamical evolution of a three-dimensional symmetric oscillator with a fractional Caputo operator. The dynamical properties of the considered model such as equilibria and its stability are also presented. The existence results and uniqueness of solutions for the suggested model are analyzed using the tools from fixed point theory. The symmetric oscillator is analyzed numerically and graphically with various fractional orders. It is observed that the fractional operator has a significant impact on the evolution of the oscillator dynamics showing that the system has a limit-cycle attractor. Offset-boosting control phenomena in the system are also studied with different orders and parameters.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 20
    Study on the Dynamics of a Piecewise Tumor-Immune Interaction Model
    (World Scientific Publ Co Pte Ltd, 2022) Saifullah, Sayed; Ahmad, Shabir; Jarad, Fahd
    Many approaches have been proposed in recent decades to represent the behaviors of certain complicated global problems appearing in a variety of academic domains. One of these issues is the multi-step behavior that some situations exhibit. Abdon and Seda devised new operators known as "piecewise operators" to deal with such problems. This paper presents the dynamics of the tumor-immune-vitamins model in the sense of a piecewise derivative. The piecewise operator considered here is composed of classical and Caputo operators. The existence and uniqueness of the solution with a piecewise derivative are presented with the aid of fixed point results. With the help of the Newton polynomial, a numerical scheme is presented for the examined model. The attained results are visualized through simulations for different fractional orders.
  • Article
    Citation - WoS: 49
    Citation - Scopus: 61
    Laplace Decomposition for Solving Nonlinear System of Fractional Order Partial Differential Equations
    (Springer, 2020) Shah, Rasool; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; Khan, Hassan
    In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo operator. The validity of the proposed method is analyzed through illustrative examples. The solution graphs have shown a close contact between the exact and LADM solutions. It is observed that the solutions of fractional-order problems converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested technique. Due to better accuracy and straightforward implementation, the extension of the present method can be made to solve other fractional-order problems.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Computational 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, Maryam
    The SARS-CoV-2 virus pandemic remains a pressing issue with its unpredictable nature, and it spreads worldwide through human interaction. Current research focuses on the investigation and analysis of fractional epidemic models that discuss the temporal dynamics of the SARS-CoV-2 virus in the community. In this work, we choose a fractional-order mathematical model to examine the transmissibility in the community of several symptoms of COVID-19 in the sense of the Caputo operator. Sensitivity analysis of R0 and disease-free local stability of the system are checked. Also, with the assistance of fixed point theory, we demonstrate the existence and uniqueness of the system. In addition, numerically we solve the fractional model and presented some simulation results via actual estimation parameters. Graphically we displayed the effects of numerous model parameters and memory indexes. The numerical outcomes show the reliability, validation, and accuracy of the scheme.
  • Article
    Citation - Scopus: 1
    Caputo-Based Model for Increasing Strains of Coronavirus: Theoretical Analysis and Experimental Design
    (World Scientific Publ Co Pte Ltd, 2022) Alshomrani, Ali S.; Baleanu, Dumitru
    One of the most severe and troubling diseases these days is COVID-19 pandemic. The COVID-19 pandemic's dangerous effects are extremely rapid, and infection normally results in death within a few weeks. As a consequence, it is important to delve deeper into the complexities of this elusive virus. In this study, we propose a Caputo-based model for increasing COVID-19 strains. The memory effect and hereditary properties of the fractional variant for the model enable us to fully comprehend the dynamics of the model's features. The existence of unique solution using the fixed-point theorem and Arzela-Ascoli principle as well as the stability analysis of the model by means of Ulam-Hyer stability (UHS) and generalized Ulam-Hyer stability (GUHS) have been discussed. Furthermore, the parameters of the model are estimated using 3 months data points chosen from Nigeria using the nonlinear least-squares technique. The best-suited parameters and the optimized Caputo fractional-order parameter a are obtained by running simulations for both models. The proposed model is shown to comprehend the dynamical behavior of the virus better than the integer-order version. In addition, to shed more light on the model's characteristics, various numerical simulations are performed using an efficient numerical scheme.
  • Article
    Citation - WoS: 37
    Citation - Scopus: 48
    An Approximate Analytical Solution of the Navier-Stokes Equations Within Caputo Operator and Elzaki Transform Decomposition Method
    (Springer, 2020) Khan, Hassan; Khan, Adnan; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; Hajira
    In this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier-Stokes equations with a Caputo fractional derivative. The numerical simulations and examples are presented to show the validity of the suggested method. The solutions are determined for the problems of both fractional and integer orders by a simple and straightforward procedure. The obtained results are shown and explained through graphs and tables. It is observed that the derived results are very close to the actual solutions of the problems. The fractional solutions are of special interest and have a strong relation with the solution at the integer order of the problems. The numerical examples in this paper are nonlinear and thus handle its solutions in a sophisticated manner. It is believed that this work will make it easy to study the nonlinear dynamics, arising in different areas of research and innovation. Therefore, the current method can be extended for the solution of other higher-order nonlinear problems.
  • Article
    Citation - WoS: 25
    Citation - Scopus: 25
    A Numerical Study of Dengue Internal Transmission Model With Fractional Piecewise Derivative
    (Elsevier, 2022) Yassen, Mansour F.; Alam, Mohammad Mahtab; Alkhati, Soliman; Jarad, Fahd; Riaz, Muhammad Bilal; Ahmad, Shabir
    The goal of this paper is to study the dynamics of the dengue internal transmission model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana-Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative is presented for the considered problem by using fixed point theorems. The suggested problem's approximate solution is demonstrated using the piecewise numerical iterative Newton polynomial approach. A numerical scheme for piecewise derivatives is established in terms of singular and non-singular kernels. The numerical simulation for the piecewise derivable problem under consideration is depicted using data for various fractional orders. This work makes the idea of piecewise derivatives and the dynamics of the crossover problem much clearer.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 17
    The Analytical Analysis of Nonlinear Fractional-Order Dynamical Models
    (Amer inst Mathematical Sciences-aims, 2021) Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; Xu, Jiabin
    The present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    On the Approximate Solution of Fractional-Order Whitham-Broer Equations
    (World Scientific Publ Co Pte Ltd, 2021) Gomez-Aguilar, J. F.; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; Khan, Hassan
    In this paper, the Homotopy perturbation Laplace method is implemented to investigate the solution of fractional-order Whitham-Broer-Kaup equations. The derivative of fractional-order is described in Caputo's sense. To show the reliability of the suggested method, the solution of certain illustrative examples are presented. The results of the suggested method are shown and explained with the help of its graphical representation. The solutions of fractional-order problems as well as integer-order problems are determined by using the present technique. It has been observed that the obtained solutions are in significant agreement with the actual solutions to the targeted problems. Computationally, it has been analyzed that the solutions at different fractional-orders have a higher rate of convergence to the solution at integer-order of the derivative. Due to the analytical analysis of the problems, this study can further modify the solution of other fractional-order problems.