Navigating climate complexity and its control via hyperchaotic dynamics in a 4D Caputo fractional model.

This interdisciplinary study critically analyzes current research, establishing a profound connection between sea water, sea ice, sea temperature, and surface temperature through a 4D hyperchaotic Caputo fractional differential equation. Emphasizing the collective impact on climate, focusing on challenges from anthropogenic global warming, the study scrutinizes theoretical aspects, including existence and uniqueness. Two sliding mode controllers manage chaos in this 4D fractional system, assessed amid uncertainties and disruptions. The global stability of these controlled systems is also confirmed, considering both commensurate and non-commensurate 4D fractional order. To demonstrate the intricate chaotic motion within the system, we employ the Lyapunov exponent and Poincare sections. Numerical simulations are conducted by using the predictor-corrector method. The effects of surface temperature on chaotic dynamics are discussed. The crucial role of sea ice reflection in climate stability is highlighted in two scenarios. Correlation graphs, comparing model and observational data using the predictor-corrector method, enhance the proposed 4D hyperchaotic model's credibility. Subsequently, numerical simulations validate theoretical assertions about the controllers' influence. These controllers indicate which variable significantly contributes to controlling the chaos.

[Formula: see text] model for analyzing [Formula: see text]-19 pandemic process via [Formula: see text]-Caputo fractional derivative and numerical simulation.

The objective of this study is to develop the [Formula: see text] epidemic model for [Formula: see text]-[Formula: see text] utilizing the [Formula: see text]-Caputo fractional derivative. The reproduction number ([Formula: see text]) is calculated utilizing the next generation matrix method. The equilibrium points of the model are computed, and both the local and global stability of the disease-free equilibrium point are demonstrated. Sensitivity analysis is discussed to describe the importance of the parameters and to demonstrate the existence of a unique solution for the model by applying a fixed point theorem. Utilizing the fractional Euler procedure, an approximate solution to the model is obtained. To study the transmission dynamics of infection, numerical simulations are conducted by using MatLab. Both numerical methods and simulations can provide valuable insights into the behavior of the system and help in understanding the existence and properties of solutions. By placing the values [Formula: see text], [Formula: see text] and [Formula: see text] instead of [Formula: see text], the derivatives of the Caputo and Caputo-Hadamard and Katugampola appear, respectively, to compare the results of each with real data. Besides, these simulations specifically with different fractional orders to examine the transmission dynamics. At the end, we come to the conclusion that the simulation utilizing Caputo derivative with the order of 0.95 shows the prevalence of the disease better. Our results are new which provide a good contribution to the current research on this field of research.

On periodic solutions of a discrete Nicholson's dual system with density-dependent mortality and harvesting terms.

In this study, we discuss the existence of positive periodic solutions of a class of discrete density-dependent mortal Nicholson's dual system with harvesting terms. By means of the continuation coincidence degree theorem, a set of sufficient conditions, which ensure that there exists at least one positive periodic solution, are established. A numerical example with graphical simulation of the model is provided to examine the validity of the main results.

The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach.

This paper deals with the existence of nonnegative solutions for a class of boundary value problems of fractional q-differential equation D q σ c [ k ] ( t ) = w ( t , k ( t ) , c D q ζ [ k ] ( t ) ) with three-point conditions for t ∈ ( 0 , 1 ) on a time scale T t 0 = { t : t = t 0 q n } ∪ { 0 } , where n ∈ N , t 0 ∈ R , and 0 < q < 1 , based on the Leray-Schauder nonlinear alternative and Guo-Krasnoselskii theorem. Moreover, we discuss the existence of nonnegative solutions. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order.

We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibrium points is investigated. We prove the existence of a unique solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. To predict the transmission of COVID-19 in Iran and in the world, we provide a numerical simulation based on real data.

Calculation of electron scattering cross sections for Anthracene, Pyridine and Warfarin molecules over energy range 10-30000 eV.

This paper reports electron impact total cross section, total elastic, total inelastic and differential cross sections for molecules Anthracene, Pyridine and Warfarin having been computed using the independent atom model with screening-corrected additivity rule over an incident energy range of 10-30000 eV. The calculations are performed with relativistic (Dirac) partial-wave for scattering by applying a local central interaction potential V(r). A model spherical complex optical potential is used for calculations. Good agreement is achieved in intermediate and high-energy zones.