Values Of Fractional Order Derivative Research Articles

COMPUTATIONAL STUDY OF FRACTIONAL-ORDER VECTOR BORNE DISEASES MODEL

In this paper, we solve a nonlinear fractional-order model for analyzing the dynamical behavior of vector-borne diseases within the frame of Caputo-fractional derivative. The proposed mathematical model advances the existing integer-order model on transmission and cure of vector-borne diseases. The existence and uniqueness of the solutions of the fractional-order model are proved using the Banach contraction principle. We investigate the local asymptomatic stability for the obtained disease-free equilibrium point and global stability for the proposed model in the sense of Ulam–Hyers stability criteria, respectively. Besides that, we obtain a numerical solution for the projected model using the Corrector-Predictor algorithm. Finally, to illustrate the obtained theoretical results, we perform numerical simulations for different values of fractional-order derivative and make a comparison with the results of the integer-order derivative.

Uncertain inverse problem for fractional dynamical systems using perturbed collage theorem

In this paper, we intend to obtain some numerical approximations of inverse problem by means of fractional differential equations under interval uncertainty. For this purpose, using perturbed Collage theorem, we achieve the approximations with the help of minimization procedure. We discuss the Picard operator and the existence with the uniqueness of solutions of interval fractional differential equations (IFDEs) using contraction mappings. Some modifications of existing results on the approximations of interval-valued functions using Schauder basis in the metric space are derived. Then, the fractional version of approximation in the Banach space is obtained to compute the numerical solution. In fact, we also employ Collage-based method for solving IFDEs with inverse problem. Finally, illustrative examples are solved in details to show that the results are in good agreement with the exact solutions for different values of fractional order derivative under generalized differentiability.

A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China.

The novel Covid-19 was identified in Wuhan China in December, 2019 and has created medical emergency world wise and distorted many life in the couple of month, it is being burned challenging situation for the medical scientist and virologists. Fractional order derivative based modeling is quite important to understand the real world problems and to analyse realistic situation of the proposed model. In the present investigation a fractional model based on Caputo-Fabrizio fractional derivative has been developed for the transmission of CORONA VIRUS (COVID-19) in Wuhan China. The existence and uniqueness solutions of the fractional order derivative has been investigated with the help of fixed point theory. Adamas- Bashforth numerical scheme has been used in the numerical simulation of the Caputo-Fabrizio fractional order derivative. The analysis of susceptible population, exposed population, infected population, recovered population and concentration of the virus of COVID-19 in the surrounding environment with respect to time for different values of fractional order derivative has been shown by means of graph. The comparative analysis has also been performed from classical model and fractional model along with the certified experimental data.

A conformable mathematical model for alcohol consumption in Spain

A study on the conformable model of alcohol consumption in Spain has been presented. For the proposed model, the existence as well as the uniqueness of the solution has been discussed with the help of fixed-point theory. An analytical technique, Variational Iteration Method (VIM), has been used to obtain the solution to the governing system of differential equations. With the help of suitable plots, the role of fractional order derivative has been highlighted. For decreasing values of fractional order derivative, decrease in the number of non-consumers and non-risk consumers has been observed. By increasing the value of fractional order derivative, a sharp decrease can be seen in the compartment of risk-consumers. The agreement between the current study and the already existing studies, with ordinary derivatives, has also been pointed out.

Response of fractional order on energy ratios at the boundary surface of fluid-piezothermoelastic media

In the present investigation, the phenomenon of reflection and transmission of plane waves from the interface between fluid half space and transversely isotropic piezothermoelastic solid half space with fractional order derivative is discussed. Energy ratios are computed with the use of amplitude ratios. The law of conservation of energy across the interface is verified. It is found that the energy ratios are the functions of angle of incidence, frequency of independent wave and depend on the different piezothermoelastic material. Cadmium selenide (CdSe) piezothermoelastic material has been considered which is in welded contact with water. Variations of energy ratios corresponding to the reflected and transmitted waves with respect to different values of fractional order derivative are shown graphically. A particular reduced case is also discussed.

Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy

In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy.

Source term in the linear analysis of FNPK equations

The aim of this work is investigate the stability effects of each term of fractional neutron point kinetics (FNPK) equations, taking special emphasis on the source term. The method applied in this work considers the transformation of the s-plane to the W-plane. Short and longs relaxation times for different values of fractional-order derivative were analyzed and the minimum absolute phase was obtained in order to establish the stability of the system. The results obtained shown that the source term are crucial in the FNPK instability.