Yazar "Saifullah, Sayed" seçeneğine göre listele

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    Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels
    (Amer Inst Mathematical Sciences-Aims, 2022) Ul Haq, Ihtisham; Ahmad, Shabir; Saifullah, Sayed; Nonlaopon, Kamsing; Akgul, Ali
    In this work, we formulate a fractal fractional chaotic system with cubic and quadratic nonlinearities. A fractal fractional chaotic Lorenz type and financial systems are studied using the Caputo Fabrizo (CF) fractal fractional derivative. This study focuses on the characterization of the chaotic nature, and the effects of the fractal fractional-order derivative in the CF sense on the evolution and behavior of each proposed systems. The stability of the equilibrium points for the both systems are investigated using the Routh-Hurwitz criterion. The numerical scheme, which includes the discretization of the CF fractal-fractional derivative, is used to depict the phase portraits of the fractal fractional chaotic Lorenz system and the fractal fractional-order financial system. The simulation results presented in both cases include the two- and three-dimensional phase portraits to evaluate the applications of the proposed operators.
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    Bifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model
    (Pergamon-Elsevier Science Ltd, 2022) Xuan, Liu; Ahmad, Shabir; Ullah, Aman; Saifullah, Sayed; Akguel, Ali; Qu, Haidong
    The association of cancer and immune cells has complex nature and produces chaotic behavior when it is simulated. The newly introduced operators which combine the fractal and fractional operators produce excellent and profound hidden attractors in a chaotic system which is sometimes not possible to get hidden attractors using integer order operators. The cancer model is considered under fractal fractional operator in Caputo sense. Linear stability of different equilibrium points is analyzed. The primary objective of the current paper is to analyze different bifurcations like pitch-fork, quasi, and inverse period-doubling bifurcations. Another important objective of this article is to study hidden limit cycle type chaotic structures of the cancer model via Caputo fractalfractional operator. The existence and uniqueness of the solution and Ulam-Hyres (UH) stability are studied through the concepts of nonlinear analysis. The numerical solution is derived through the predictor-corrector method. The obtained results were presented and validated through numerical simulations. The lyapunov spectra of the state variables are presented through graphical illustration and table. Sensitivity of the state variables to the initial conditions are simulated for initial conditions 0.1 and 0.11. For various values of fractal dimensions and fractional orders, the time series oscillations and hidden limit cycles type chaotic attractors are graphically presented through MATLAB-17.
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    Crossover Dynamics of Rotavirus Disease under Fractional Piecewise Derivative with Vaccination Effects: Simulations with Real Data from Thailand, West Africa, and the US
    (Mdpi, 2022) Naowarat, Surapol; Ahmad, Shabir; Saifullah, Sayed; De la Sen, Manuel; Akguel, Ali
    Many diseases are caused by viruses of different symmetrical shapes. Rotavirus particles are approximately 75 nm in diameter. They have icosahedral symmetry and particles that possess two concentric protein shells, or capsids. In this research, using a piecewise derivative framework with singular and non-singular kernels, we investigate the evolution of rotavirus with regard to the effect of vaccination. For the considered model, the existence of a solution of the piecewise rotavirus model is investigated via fixed-point results. The Adam-Bashforth numerical method along with the Newton polynomial is implemented to deduce the numerical solution of the considered model. Various versions of the stability of the solution of the piecewise rotavirus model are presented using the Ulam-Hyres concept and nonlinear analysis. We use MATLAB to perform the numerical simulation for a few fractional orders to study the crossover dynamics and evolution and effect of vaccination on rotavirus disease. To check the validity of the proposed approach, we compared our simulated results with real data from various countries.
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    Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis
    (Elsevier, 2023) Iskakova, Kulpash; Alam, Mohammad Mahtab; Ahmad, Shabir; Saifullah, Sayed; Akguel, Ali; Yilmaz, Guelnur
    In this article, a new nonlinear four-dimensional hyperchaotic model is presented. The dynamical aspects of the complex system are analyzed covering equilibrium points, linear stability, dissipation, bifurcations, Lyapunov exponent, phase portraits, Poincare mapping, attractor projection, sensitivity and time series analysis. To analyze hidden attractors, the proposed system is investigated through nonlocal operator in Caputo sense. The existence of solution of the system in fractional sense is studied by fixed point theory. The stability of fractional order system is demonstrated via Matignon stability criteria. The fractional order system is numerically studied via newly developed numerical method which is based on Newton polynomial interpolation. The evolution of the attractors are depicted with different fractional orders. For few fractional orders, some hidden strange chaotic attractors are observed through graphs. Theoretical and numerical studies demonstrate that this model has complex dynamics with some stimulating physical characteristics. To verify and validate the results, we implement Field Programmable Analog Arrays (FPAA).(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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    Fractional generalized perturbed KdV equation with a power Law kernel: A computational study
    (Elsevier, 2023) Shehzada, Khan; Ullah, Aman; Saifullah, Sayed; Akgul, Ali
    In this study, we analyze the nonlinear generalized perturbed KdV equation using the Shehu transform and decomposition approach to obtain solutions. Multiple cases with appropriate initial conditions demonstrate the procedure's effectiveness and validity, with excellent agreements noted. Simulations reveal three distinct solutions: one bright-soliton, two wave solutions, and dark -bright soliton solutions. Fractional order significantly impacts wave amplitudes and nonlinearity characteristics, affecting system excitations. These findings offer insights into complex behaviors, with potential applications in fluid dynamics, nonlinear optics, and plasma physics, guiding experimental design and system analysis.
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    New waves solutions of a nonlinear Landau-Ginzburg-Higgs equation: The Sardar-subequation and energy balance approaches
    (Elsevier, 2023) Ahmad, Shafiq; Mahmoud, Emad E.; Saifullah, Sayed; Ullah, Aman; Ahmad, Shabir; Akgul, Ali; El Din, Sayed M.
    This article investigates the significance of the unsteady nonlinear Landau-Ginzburg-Higgs equation in the context of superfluids and Bose-Einstein condensates. The problem of interest is the search for new exact solutions within this equation. To tackle this problem, the Sardar-subequation and energy balance approaches are employed. Through these methods, a variety of new exact solutions are obtained, expressed in terms of cosine functions, generalized hyperbolic functions, and generalized trigonometric functions. The obtained solutions encompass different types of solitons, including bright and dark solitons, singular periodic soliton, and hybrid solitons. The solutions are then visualized through 2D and 3D simulations. The findings of this study contribute to the understanding of the Landau-Ginzburg-Higgs equation and its application to superfluids and Bose-Einstein condensates. The novelty of this work lies in the utilization of the Sardar-subequation and energy balance approaches to obtain diverse traveling wave solutions, surpassing previous efforts in the literature.
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    Nonlinear Schrodinger equation under non-singular fractional operators: A computational study
    (Elsevier, 2022) Khan, Asif; Ali, Amir; Ahmad, Shabir; Saifullah, Sayed; Nonlaopon, Kamsing; Akgul, Ali
    In this article, we present study on time fractional nonlinear Schrodinger equation. We investigate the behaviour of the aforesaid equation in two numerous types of operators having non-singular kernels, which are Atangana-Baleanu and Caputo-Fabrizio operators both considered in Caputo's sense. The considered operators are very useful as they present tremendous dynamics of the suggested equation. We obtain numerical and analytical solutions of the proposed equation under the aforementioned fractional operators by modified double Laplace transform. We present the error analysis of the suggested scheme, where we observed that the considered system primarily depend on time. When time is small, we obtain very small error between the exact and approximate solutions. For the efficiency of our considered scheme, we present some examples. Further, we present the graphical and numerical analysis of the scheme used for the solution.
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    Oscillatory and complex behaviour of Caputo-Fabrizio fractional order HIV-1 infection model
    (Amer Inst Mathematical Sciences-Aims, 2022) Ahmad, Shabir; Ullah, Aman; Partohaghighi, Mohammad; Saifullah, Sayed; Akgul, Ali; Jarad, Fahd
    HIV-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.