Estimate for Initial MacLaurin Coefficients of Certain Subclasses of Bi-univalent Functions

In this paper, estimates for second and third MacLaurin coefficients of certain subclasses of bi-univalent functions in the open unit disk defined by convolution are determined, and certain special cases are also indicated. The main result extends and improve a recent one obtained by Srivastava et al

Mathematical Modeling of COVID-19 Transmission Using a Fractional Order Derivative

In this article, the mathematical model of COVID-19 is analyzed in the sense of a fractional order Caputo operator with the consideration of an asymptomatic class. The suggested model is comprised of four compartments. The results from fixed point theory are used to theoretically analyze the existence and uniqueness of solution of the model in fractional perspective. For the numerical approximation of the suggested problem, a numerical iterative scheme is used, which is based on the Newton polynomial interpolation. For the efficiency and applicability of the suggested technique with a fractional Caputo operator, we simulate the results for various fractional orders

Chaos on the Vallis Model for El Niño with Fractional Operators

The Vallis model for El Niño is an important model describing a very interesting physical problem. The aim of this paper is to investigate and compare the models using both integer and non-integer order derivatives. We first studied the model with the local derivative by presenting for the first time the exact solution for equilibrium points, and then we presented the exact solutions with the numerical simulations. We further examined the model within the scope of fractional order derivatives. The fractional derivatives used here are the Caputo derivative and Caputo–Fabrizio type. Within the scope of fractional derivatives, we presented the existence and unique solutions of the model. We derive special solutions of both models with Caputo and Caputo–Fabrizio derivatives. Some numerical simulations are presented to compare the models. We obtained more chaotic behavior from the model with Caputo–Fabrizio derivative than other one with local and Caputo derivative. When compare the three models, we realized that, the Caputo derivative plays a role of low band filter when the Caputo–Fabrizio presents more information that were not revealed in the model with local derivative

Modeling the potential energy field caused by mass density distribution with Eton approach

A new approach for modeling real world problems called the “Eton Approach” was presented in this paper. The "Eton approach" combines both the concept of the variable order derivative together with Atangana derivative with memory derivative. The Atangana derivative with memory is used to account for the memory and fractional derivative for its filter effect. The approach was used to describe the potential energy field that is caused by a given charge or mass density distribution.We solve the modified model numerically and present supporting numerical simulations

Generalized groundwater plume with degradation and rate-limited sorption model with Mittag-Leffler law

The concept of differentiation with the generalized Mittag-Leffler law is used in this paper to construct the model of movement of groundwater pollution with degradation and limited sorption. The fractional differentiation used in the model is in Riemann-Liouville sense. The new model is solved analytically using the Green Laplace transform approach. A numerical scheme is used to obtain the numerical solution of the modified model. Keywords: Movement of groundwater pollution, Plume with degradation, Rate-limited sorption, Atangana-Baleanu derivative in Riemann-Liouville sens

Analysis of the Keller–Segel Model with a Fractional Derivative without Singular Kernel

Using some investigations based on information theory, the model proposed by Keller and Segel was extended to the concept of fractional derivative using the derivative with fractional order without singular kernel recently proposed by Caputo and Fabrizio. We present in detail the existence of the coupled-solutions using the fixed-point theorem. A detailed analysis of the uniqueness of the coupled-solutions is also presented. Using an iterative approach, we derive special coupled-solutions of the modified system and we present some numerical simulations to see the effect of the fractional order

Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel

We presented the model of resistance, inductance, capacitance circuit using a novel derivative with fractional order that was recently proposed by Caputo and Fabrizio. The derivative possesses more important characteristics that are very useful in modelling. In this article, we proposed a novel translation from ordinary equation to fractional differential equation. Using this novel translation, we modified the resistance, inductance, capacitance electricity model. We solved analytically the modified equation using the Laplace transform method. We presented numerical results for different values of the fractional order. We observed that this solution depends on the fractional order