Yazar "Conejero, J. Alberto" seçeneğine göre listele
Listeleniyor 1 - 5 / 5
Sayfa Başına Sonuç
Sıralama seçenekleri
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 Fractal Fractional Derivative Models for Simulating Chemical Degradation in a Bioreactor(Mdpi, 2024) Akgul, Ali; Conejero, J. AlbertoA three-differential-equation mathematical model is presented for the degradation of phenol and p-cresol combination in a bioreactor that is continually agitated. The stability analysis of the model's equilibrium points, as established by the study, is covered. Additionally, we used three alternative kernels to analyze the model with the fractal-fractional derivatives, and we looked into the effects of the fractal size and fractional order. We have developed highly efficient numerical techniques for the concentration of biomass, phenol, and p-cresol. Lastly, numerical simulations are used to illustrate the accuracy of the suggested method.Öğe Predictive deep learning models for analyzing discrete fractional dynamics from noisy and incomplete data(Elsevier, 2024) Garibo-i-Orts, Oscar; Lizama, Carlos; Akgul, Ali; Conejero, J. AlbertoWe study the accuracy of machine learning methods for inferring the parameters of noisy fractional Wu-Baleanu trajectories with some missing initial terms. Our model is based on a combination of convolutional and recurrent neural networks (LSTM), which permits the extraction of characteristics from trajectories while preserving time dependency. We show that these approach exhibit good accuracy results despite the poor quality of the data.Öğe Qualitative Analysis of Stochastic Caputo-Katugampola Fractional Differential Equations(Mdpi, 2024) Khan, Zareen A.; Liaqat, Muhammad Imran; Akgul, Ali; Conejero, J. AlbertoStochastic pantograph fractional differential equations (SPFDEs) combine three intricate components: stochastic processes, fractional calculus, and pantograph terms. These equations are important because they allow us to model and analyze systems with complex behaviors that traditional differential equations cannot capture. In this study, we achieve significant results for these equations within the context of Caputo-Katugampola derivatives. First, we establish the existence and uniqueness of solutions by employing the contraction mapping principle with a suitably weighted norm and demonstrate that the solutions continuously depend on both the initial values and the fractional exponent. The second part examines the regularity concerning time. Third, we illustrate the results of the averaging principle using techniques involving inequalities and interval translations. We generalize these results in two ways: first, by establishing them in the sense of the Caputo-Katugampola derivative. Applying condition beta=1, we derive the results within the framework of the Caputo derivative, while condition beta -> 0+ yields them in the context of the Caputo-Hadamard derivative. Second, we establish them in Lp space, thereby generalizing the case for p=2.Öğe Revised and Generalized Results of Averaging Principles for the Fractional Case(Mdpi, 2024) Liaqat, Muhammad Imran; Khan, Zareen A.; Conejero, J. Alberto; Akgul, AliThe averaging principle involves approximating the original system with a simpler system whose behavior can be analyzed more easily. Recently, numerous scholars have begun exploring averaging principles for fractional stochastic differential equations. However, many previous studies incorrectly defined the standard form of these equations by placing epsilon in front of the drift term and epsilon in front of the diffusion term. This mistake results in incorrect estimates of the convergence rate. In this research work, we explain the correct process for determining the standard form for the fractional case, and we also generalize the result of the averaging principle and the existence and uniqueness of solutions to fractional stochastic delay differential equations in two significant ways. First, we establish the result in Lp space, generalizing the case of p=2. Second, we establish the result using the Caputo-Katugampola operator, which generalizes the results of the Caputo and Caputo-Hadamard derivatives.
