The Enzymatic control reactions model was presented within the scope of fractional calculus. In order to accommodate the usual initial conditions, the fractional derivative used is in Caputo sense. The methodologies of the three analytical methods were used to derive approximate solution of the fractional nonlinear system of differential equations. Two methods use integral operator and the other one uses just an integral. Numerical results obtained exhibit biological behavior of real world problem.

Ante el gran interés suscitado en nuestros días por la Es- cuela de Constanza y la Estética de la Recepción que le es propia, propone- mos un ensayo introductorio de alta di- vulgación, que haga contactar al lector no iniciado con la riqueza literaria y hu- manística de la susodicha Escuela, y de sus dos grandes pensadores: H. R. Jauss y W. Iker. Desde esta perspectiva jausista, presentamos los tres ángeles bíblicos por excelencia: el ángel de Ja- cob, el ángel (...) de Getsemaní, y el texto paulino de 2Cor 12, con el doblón meta- fórico del “aguijón en la carne” en el “ángel de Satanás”, que adquieren así un particular relieve y significatividad en los pintores Gauguin y Picasso. (shrink)

Hopfield neural network is considered as an artificial model derived from the brain structures and it is an important model that admits an adequate performance in neurocomputing. In this article, we solve a dynamical model of 3D HNNs via Atangana–Baleanu fractional derivatives. To find the numerical solution of the considered dynamical model, the well-known Predictor-Corrector method is used. A number of cases are taken by using two different sets of values of the activation gradient of the neurons as well (...) as six different initial conditions. The given results have been perfectly established using the different fractional-order values on the given derivative operator. The objective of this research is to investigate the dynamics of the proposed HNN model at various values of fractional orders. Nonlocal characteristic of the AB derivative contains the memory in the system which is the main motivation behind the proposal of this research. (shrink)

In this article, we solve nonlinear systems of third order KdV Equations and the systems of coupled Burgers equations in one and two dimensions with the help of two different methods. The suggested techniques in addition with Laplace transform and Atangana–Baleanu fractional derivative operator are implemented to solve four systems. The obtained results by implementing the proposed methods are compared with exact solution. The convergence of the method is successfully presented and mathematically proved. The results we get are compared (...) with exact solution through graphs and tables which confirms the effectiveness of the suggested techniques. In addition, the results obtained by employing the proposed approaches at different fractional orders are compared, confirming that as the value goes from fractional order to integer order, the result gets closer to the exact solution. Moreover, suggested techniques are interesting, easy, and highly accurate which confirm that these methods are suitable methods for solving any partial differential equations or systems of partial differential equations as well. (shrink)

In this paper, DSEK model with fractional derivatives of the Atangana-Baleanu Caputo is proposed. This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DSEK model. According to this theory, we will define two operators based on Lipschitzian and prove that they are contraction mapping and relatively compact. Ulam-Hyers stability theorem is implemented to prove the fractional DSEK model’s (...) stability in Banach space. Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α ∈ 0,1 and different step sizes h. Result discussion will be given, describing the changes that occur due to the step size h. (shrink)

In this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate-analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method’s usefulness. Fractional-order solutions are the most in line with the dynamics of the targeted problems, and they provide an (...) endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology. (shrink)

Excessive use of social media is a developing concern in the twenty-first century. This issue needs to be addressed before it has any more significant consequences than what we are currently experiencing. As a preventive technique, advertisements and awareness-raising campaigns about the detrimental impact of digital technologies are used. The application of novel mathematical techniques and terminologies in this field of study will have significant potential to enhance healthy living by preventing certain ailments. This is the most compelling justification for (...) conducting a new study with the most up-to-date techniques at our disposal. This study investigates clear and concise transmission in order to generate a deterministic mathematical model of social media addiction S M A using the fractal-fractional derivative operator. Also, the analysis of the S M A model in terms of the invariant domain, the existence of a positive invariant solution, and equilibria assumptions are stated in a detailed manner. Besides that, the basic reproduction number ℝ 0 < 1 is computed, demonstrating that the proposed methodology is more efficacious. The Atangana-Baleanu FF differential operators are recently defined in FF differential operators that are applied to characterize the S M A model’s mathematical algorithm. We investigated the numerical behaviour of the S M A in three ways: changing the fractional-order α as well as the fractal-dimension ℘ ; changing α while keeping ℘ constant; and changing ℘ while keeping α constant. Our examined visualizations and simulation studies using MATLAB for the numerical modelling of the aforementioned system showed that the novel developed Atangana-Baleanu FF differential operators produce remarkable results when compared to the classical frame. (shrink)

In this article, we investigated a deterministic model of pneumonia-meningitis coinfection. Employing the Atangana–Baleanu fractional derivative operator in the Caputo framework, we analyze a seven-component approach based on ordinary differential equations. Furthermore, the invariant domain, disease-free as well as endemic equilibria, and the validity of the model’s potential results are all investigated. According to controller design evaluation and modelling, the modulation technique devised is effective in diminishing the proportion of incidences in various compartments. A fundamental reproducing value is generated (...) by exploiting the next generation matrix to assess the properties of the equilibrium. The system’s reliability is further evaluated. Sensitivity analysis is used to classify the impact of each component on the spread or prevention of illness. Using simulation studies, the impacts of providing therapy have been determined. Additionally, modelling the appropriate configuration demonstrated that lowering the fractional order from 1 necessitates a rapid initiation of the specified control technique at the largest intensity achievable and retaining it for the bulk of the pandemic’s duration. (shrink)