Yazar "Alqahtani, Rubayyi T." seçeneğine göre listele

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    A New Application of the Sumudu Transform for the Falling Body Problem
    (Hindawi Ltd, 2021) Akgul, Esra Karatas; Akgul, Ali; Alqahtani, Rubayyi T.
    In this study, we investigate the falling body problem with three different fractional derivatives. We acquire the solutions of the model by the Sumudu transform. We show the accuracy of the Sumudu transform by some theoretic results and implementations.
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    Dynamical Analysis of Bio-Ethanol Production Model under Generalized Nonlocal Operator in Caputo Sense
    (Mdpi, 2021) Alqahtani, Rubayyi T.; Ahmad, Shabir; Akguel, Ali
    The nonlinear fractional-order model of bioethanol production under a generalized nonlocal operator in the Caputo sense is investigated in this work. Theoretical and computational aspects of the considered model are discussed. We prove that the model has at least one solution and a unique solution using the Leray-Schauder and Banach contraction theorems. Using functional analysis, we investigate several types of Ulam-Hyres model stability. We use the predictor-corrector (P-C) method to construct a broad numerical scheme for the model's solution. The proposed numerical method's stability is demonstrated. Finally, we depict the numerical findings geometrically to demonstrate the model's dynamics.
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    Effect of vaccination to control COVID-19 with fractal fractional operator
    (Elsevier, 2022) Amin, Maryam; Farman, Muhammad; Akgul, Ali; Alqahtani, Rubayyi T.
    Currently, Atangana proposed new fractal-fractional operators that had extensively used to observe the unpredictable elements of an issue. COVID-19 is a pervasive infection today and is hard to fix. In this structure, the novel operators have been used to observing the effect of vaccination in the COVID-19 model with different values of eta(1), eta(2) which are used to show the effect of vaccination. The system will be converted into disease-free according to reproductive number. We used the Atangana-Baleanu fractal-fractional operator to investigate the COVID-19 model qualitatively and quantitatively. By using fixed point theorems we proved the existence and uniqueness of the model with the Atangana-Baleanue fractal- fractional operator. A non-linear assessment helped to find out the stability of the Ulam-Hyres. We simulate the mathematical outcomes, to understand the relationship of operators in several senses, for numerous arrangements of fractional and fractal orders. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
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    investigating nonlinear fractional systems: reproducing kernel Hilbert space method
    (Springer, 2024) Attia, Nourhane; Akgul, Ali; Alqahtani, Rubayyi T.
    The reproducing kernel Hilbert space method (RK-HS method) is used in this research for solving some important nonlinear systems of fractional ordinary differential equations, such as the fractional Susceptible-Infected-Recovered (SIR) model. Nonlinear systems are widely used across various disciplines, including medicine, biology, technology, and numerous other fields. To evaluate the RK-HS method's accuracy and applicability, we compare its numerical solutions with those obtained via Hermite interpolation, the Adomian decomposition method, and the residual power series method. To further support the reliability of the RK-HS method, the convergence analysis is discussed.
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    Mathematical Analysis of Biodegradation Model under Nonlocal Operator in Caputo Sense
    (Mdpi, 2021) Alqahtani, Rubayyi T.; Ahmad, Shabir; Akguel, Ali
    To lower the concentration of organic pollutants in the effluent stream, wastewater must be treated before being discharged into the environment. The question of whether wastewater treatment facilities can successfully reduce the concentration of micropollutants found in their influent streams is becoming increasingly pressing. The removal of micropollutants in treatment plants is investigated using a model that incorporates biodegradation and sorption as the key processes of micropollutant removal. This article provides the mathematical analysis of the wastewater model that describes the removal of micropollutant in treatment plants under a non-local operator in Caputo sense. The positivity of the solution is presented for the Caputo fractional model. The steady state's solution of model and their stability is presented. The fixed point theorems of Leray-Schauder and Banach are used to deduce results regarding the existence of the solution of the model. Ulam-Hyers (UH) types of stabilities are presented via functional analysis. The fractional Euler method is used to find the numerical results of the proposed model. The numerical results are illustrated via graphs to show the effects of recycle ratio and the impact of fractional order on the evolution of the model.
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    New Type Modelling of the Circumscribed Self-Excited Spherical Attractor
    (Mdpi, 2022) Partohaghighi, Mohammad; Akgul, Ali; Alqahtani, Rubayyi T.
    The fractal-fractional derivative with the Mittag-Leffler kernel is employed to design the fractional-order model of the new circumscribed self-excited spherical attractor, which is not investigated yet by fractional operators. Moreover, the theorems of Schauder's fixed point and Banach fixed existence theory are used to guarantee that there are solutions to the model. Approximate solutions to the problem are presented by an effective method. To prove the efficiency of the given technique, different values of fractal and fractional orders as well as initial conditions are selected. Figures of the approximate solutions are provided for each case in different dimensions.
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    On Numerical Analysis of Bio-Ethanol Production Model with the Effect of Recycling and Death Rates under Fractal Fractional Operators with Three Different Kernels
    (Mdpi, 2022) Alqahtani, Rubayyi T.; Ahmad, Shabir; Akgul, Ali
    The main metabolism of yeasts produces bioethanol. Bioethanol, which is produced from biomass and bioenergy crops, has been promoted as one of the most viable alternatives to fossil fuels. The following reaction represents all of the knowledge we have regarding intracellular reactions and their regulatory mechanisms: biomass + substrates -> ethanol + biomass (more cells). Atangana has suggested new operators based on a combination of fractional and fractal calculus. Fractal-fractional operators (FFOs) have frequently been utilized to investigate the dynamics of a physical problem. In this paper, FFOs are used to investigate a nonlinear mathematical model for ethanol production with three different kernels. Famous fixed point results are employed to show the existence and uniqueness of the solution of the FFO ethanol model under the Mittag-Leffler kernel. The concept of non-linear analysis is utilized to demonstrate the model's Ulam-Hyres stability. The Adams- Bashforth numerical technique, which is based on the Lagrangian interpolation method, is utilized to find the solution of the model under fractal-fractional operators with three different kernels. The numerical results are simulated with MATLAB-17 for several sets of fractional orders and fractal dimensions to show the relationship between components of ethanol production under new operators in various senses.