Caputo-Fabrizio Fractional Derivative Research Articles

Fractal fractional-order derivative for HIV/AIDS model with Mittag-Leffler kernel

In this paper, HIV/AIDS fractional-order model is studied. This epidemic phenomenon is analyzed using Caputo-Fabrizio and Fractal fractional derivative operator that includes an antiretroviral treatment compartment. The advanced approach is used for HIV/AIDS fractional-order model to get reliable outcomes with the help of sumudu transform. The fractional-order HIV/AIDS model is analyzed qualitatively as well as verify unique solutions. Numerical simulations are performed to explain the effects of changing the fractional-order and to support the theoretical results using proposed methods for a range of fractional orders. Also, the comparison has been made with classical order derivative to check the effectiveness of the proposed method for HIV/AIDS.

Mathematical modeling of COVID-19 pandemic in India using Caputo-Fabrizio fractional derivative

The range of effectiveness of the novel corona virus, known as COVID-19, has been continuously spread worldwide with the severity of associated disease and effective variation in the rate of contact. This paper investigates the COVID-19 virus dynamics among the human population with the prediction of the size of epidemic and spreading time. Corona virus disease was first diagnosed on January 30, 2020 in India. From January 30, 2020 to April 21, 2020, the number of patients was continuously increased. In this scientific work, our main objective is to estimate the effectiveness of various preventive tools adopted for COVID-19. The COVID-19 dynamics is formulated in which the parameters of interactions between people, contact tracing, and average latent time are included. Experimental data are collected from April 15, 2020 to April 21, 2020 in India to investigate this virus dynamics. The Genocchi collocation technique is applied to investigate the proposed fractional mathematical model numerically via Caputo-Fabrizio fractional derivative. The effect of presence of various COVID parameters e.g. quarantine time is also presented in the work. The accuracy and efficiency of the outputs of the present work are demonstrated through the pictorial presentation by comparing it to known statistical data. The real data for COVID-19 in India is compared with the numerical results obtained from the concerned COVID-19 model. From our results, to control the expansion of this virus, various prevention measures must be adapted such as self-quarantine, social distancing, and lockdown procedures.

MODELING AND APPLICATIONS OF FRACTIONAL-ORDER MUTUAL INDUCTANCE BASED ON ATANGANA–BALEANU AND CAPUTO–FABRIZIO FRACTIONAL DERIVATIVES

Many electrical systems can be characterized more authentically by fractional-order dynamic systems. The Atangana–Baleanu and the Caputo–Fabrizio fractional derivatives have solved the singularity problem in Caputo derivative. This work uses Atangana–Baleanu and Caputo–Fabrizio fractional derivatives to model the fractional-order mutual inductance in the frequency domain. To use the fractional mutual inductance in circuit design, the T-model equivalent circuits are presented with different fractional derivatives. The fractional impedance matching networks based on proposed fractional mutual coupling circuits are simulated as an application. The impedance characteristics of networks with different fractional orders are analyzed. The results indicate that the proposed fractional mutual coupling circuits based on Atangana–Baleanu and Caputo–Fabrizio fractional derivatives can be applied to the complex electrical systems to increase the design degree of freedom, which provides more choices for describing the nonlinear characteristics of the system.

Magneto-thermoelastic behaviour of a finite viscoelastic rotating rod by incorporating Eringen’s theory and heat equation including Caputo–Fabrizio fractional derivative

Magneto-thermoelastic behaviour of a finite viscoelastic rotating rod by incorporating Eringen’s theory and heat equation including Caputo–Fabrizio fractional derivative

Formula omitted]-Choquet integral on time scales with applications

The fundamental purpose of this work is to analyze Δ-Choquet integrals on time scales which is a special case of Choquet integral on abstract fuzzy (non-additive) measure space. We first present a Δ-Choquet integral with respect to non-additive Δ-measure or more precisely a distorted Lebesgue Δ-measure on an arbitrary time scale. Consequently, we come up with a more general integral than the standard Choquet integral of continuous and discrete calculus. Its use can be seen as convenient in economics, decision making, artificial intelligence, and many more. Particularly, in economics, most of the models are dynamic models (continuous and/or discrete), and those can be easily studied on time scales. Further, some basic essential results and properties of the general integral are studied. For instance, we discuss translation, homogeneity, linearity, and many more with respect to the functions and measures of the integral.Then, after that, we present some theorems for computing the integral. The findings agree to unify and extend a number of well-known results reported in the literature to a broader calculus, including continuous, discrete, and quantum calculus, among others. We also evaluate the integral on an invariant under the translation of time scales. Besides, a short note on Δ-Choquet integral with the Caputo-Fabrizio fractional derivative on the time scales is given. The significance of the outcomes is also further enhanced by a variety of interesting examples.Moreover, eventually, we stop findings after discussing an another way to calculate the Δ-Choquet integral on the time scales. To do this, we define Stieltjes distorted types-I and II Lebesgue Δ-measures on time scales which are accomplished with the help of distorted Lebesgue Δ-measure.

Analytic study of pine wilt disease model with Caputo–Fabrizio fractional derivative

In this paper, we construct an analytical study of the epidemic pine wilt disease model in a Caputo–Fabrizio type fractional order; the basic properties of the fractional differential equation and the model are presented; we give the basic properties of the model. Applying the homotopy analysis transform method to obtain numerical solutions to the model, the numerical result represented in graphs is presented.

Thermal applications of copper oxide, silver, and titanium dioxide nanoparticles via fractional derivative approach

The recent progress in nanotechnology developed more stable nanofluid models with ultra-high thermal performances. The immersion of hybrid nanoparticles in the base fluid presents novel applications in the thermal transport processes, solar energy, engineering devices, and heating systems. This continuation identified the thermal outcomes of the hybrid nanofluid model with the water base fluid. The thermal investigation is encountered by utilizing the copper oxide (CuO), silver (Ag), and titanium dioxide (TiO2) nanoparticles. The thermal selection of these three types of nanoparticles is associated with impressive characteristics and stability. To attain the more progressive thermal aspects, thermal radiation consequences are also focused. The inclined infinite configuration is assumed where these nanoparticles and base fluid are specified. The comparative results for the hybrid nanofluid and modified hybrid models are pronounced. The fractional model of dimensionless partial differential leading equations is formulated by following the recent definitions of fractional derivatives, namely, Atangana–Baleanu and Caputo–Fabrizio fractional derivatives. The semi-analytical simulations are performed via the Laplace technique for nanoparticles temperature and velocity inspection. The significances of the fractional parameter and volume fraction are observed for the velocity profile.

A numerical scheme for solving a class of time fractional integro-partial differential equations with Caputo–Fabrizio derivative

In this paper, we find the numerical solution of the time-fractional partial integro-differential equation with Caputo–Fabrizio fractional derivative. The problem is discretized by some finite difference schemes in the time direction, and then the Sinc collocation method is applied to the resulting problems in the spatial direction. The convergence and stability of the method are proved and illustrated by three test examples.

Dynamical analysis of the transmission of dengue fever via Caputo-Fabrizio fractional derivative

In this work, we develop a sophisticated mathematical model for dengue transmission dynamics based on vaccination, reinfection and carrier class assumptions. We utilize Caputo-Fabrizio fractional framework to represent the transmission phenomena of dengue. For the model analysis, the basic theory and findings of the Caputo-Fabrizio fractional operator are provided. We utilize the next-generation approach to calculate the threshold parameter R0 for our proposed dengue infection model. We have shown that the disease-free steady-state of the hypothesized dengue system is locally asymptotically stable if R0<1 and is unstable in other conditions. The reproduction number of the system of dengue infection is investigated numerically. Furthermore, under the Caputo-Fabrizio approach, we offer a numerical approach for solving our fractional-order problem. We obtain the solution pathways of our system with various values of fractional-order ϑ and other input values in order to illustrate the effects of fractional-order ϑ and other input values on our system. Based on our findings, we forecast the most essential system factors for eradicating dengue infections.

Periodic Solution of Caputo-Fabrizio Fractional Integro–differential Equation with Periodic and Integral Boundary Conditions

In this paper, we study a new approach of investigation of existence, uniqueness and stability of the periodic solution of the nonlinear fractional integro-differential equation of type Caputo-Fabrizio fractional derivative with the initial condition, periodic boundary conditions, and integral boundary conditions by using successive approximations method and Banach fixed point theorem. Finally, some examples are present to illustrate the theorems.

Analytical Solution for Impact of Caputo-Fabrizio Fractional Derivative on MHD Casson Fluid with Thermal Radiation and Chemical Reaction Effects

Fractional derivatives have been proven to showcase a spectrum of solutions that is useful in the fields of engineering, medical, and manufacturing sciences. Studies on the application of fractional derivatives on fluid flow are relatively new, especially in analytical studies. Thus, geometrical representations for fractional derivatives in the mechanics of fluid flows are yet to be discovered. Nonetheless, theoretical studies will be useful in facilitating future experimental studies. Therefore, the aim of this study is to showcase an analytical solution on the impact of the Caputo-Fabrizio fractional derivative for a magnethohydrodynamic (MHD) Casson fluid flow with thermal radiation and chemical reaction. Analytical solutions are obtained via Laplace transform through compound functions. The obtained solutions are first verified, then analysed. It is observed from the study that variations in the fractional derivative parameter, α, exhibits a transitional behaviour of fluid between unsteady state and steady state. Numerical analyses on skin friction, Nusselt number, and Sherwood number were also analysed. Behaviour of these three properties were in agreement of that from past literature.

A fractional mathematical modeling of protectant and curative fungicide application

Fungicides are consumed to foreclose or slow the epidemics of disease germ by fungi. Crop cultivation is a favorable business platform for farmers, but it is also very common for them to have losses. These losses happen by attacking pathogens, such as fungi, oomycetes (water fungi), viruses, bacteria, nematodes, and viroid that spread the infection into the plants. In this article, we derive a fractional mathematical model for simulating the dynamics of fungicide application via Caputo-Fabrizio fractional derivative. Caputo-Fabrizio operator is defined with non-singular type kernel which is better than singular kernel. We give some important proofs related to the existence of a unique solution of the given model. We derive the solution of the model by using the Adams-Bashforth algorithm and also mentioned the stability of the method. We plotted the number of graphs at different fungicide application rate, fungicide decay rate, fungicide effectiveness, curatives rate of fungicide, growth rate of the host, and removal rate. A complete structure of the given problem can be understood by this paper. The main novelty of this work is to understand the role of fungicide application in the disease caused by fungi with the help of fractional derivatives consisting memory effects.

Solutions of some typical nonlinear differential equations with Caputo-Fabrizio fractional derivative

&lt;abstract&gt;&lt;p&gt;In this paper, the solutions of some typical nonlinear fractional differential equations are discussed, and the implicit analytical solutions are obtained. The fractional derivative concerned here is the Caputo-Fabrizio form, which has a nonsingular kernel. The calculation results of different fractional orders are compared through images. In addition, by comparing the results obtained in this paper with those under Caputo fractional derivative, it is found that the solutions change relatively gently under Caputo-Fabrizio fractional derivative. It can be concluded that the selection of appropriate fractional derivatives and appropriate fractional order is very important in the modeling process.&lt;/p&gt;&lt;/abstract&gt;

Local Discontinuous Galerkin Method for the Time-Fractional KdV Equation with the Caputo-Fabrizio Fractional Derivative

This paper studies the time-fractional Korteweg-de Vries (KdV) equations with Caputo-Fabrizio fractional derivatives. The scheme is presented by using a finite difference method in temporal variable and a local discontinuous Galerkin method (LDG) in space. Stability and convergence are demonstrated by a specific choice of numerical fluxes. Finally, the efficiency and accuracy of the scheme are verified by numerical experiments.

Evaluation of regularized long-wave equation via Caputo and Caputo-Fabrizio fractional derivatives

&lt;abstract&gt;&lt;p&gt;The analytical solution of fractional-order regularized long waves in the context of various operators is presented in this study as a framework for the homotopy perturbation transform technique. To investigate regularized long wave equations, we first establish the Yang transform of the fractional Caputo and Caputo-Fabrizio operators. The fractional order regularized long wave equation is solved using the Yang transform as well. The accuracy of the proposed operators are verified using numerical problems, and the resulting solutions are shown in the figures. The solutions demonstrate how the suggested approach is accurate and suitable for analyzing nonlinear physical and engineering challenges.&lt;/p&gt;&lt;/abstract&gt;

Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative

&lt;abstract&gt;&lt;p&gt;This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of Krasnoselskii's fixed-point theorem and Banach's contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results.&lt;/p&gt;&lt;/abstract&gt;

A new result for fractional differential equation with nonlocal initial value using Caputo-Fabrizio derivative

In this paper, using Caputo-Fabrizio fractional derivative, we obtain some new results for the existence and uniqueness of solutions of differential equation with nonlocal initial value about fractional order 0 &lt; ? &lt; 1 . These results are applied with the help of Arzela-Ascoli theorem and Schauder fixed point. Also based on some ?-contractive maps for such problems, some new unique theorem has been introduced and proved. Finally, some illustrative example is considered to show the effectiveness of the results.

Semi-analytic solutions of nonlinear multidimensional fractional differential equations.

In this paper, the Adomian decomposition method (ADM) and Picard technique are used to solve a class of nonlinear multidimensional fractional differential equations with Caputo-Fabrizio fractional derivative. The main advantage of the Caputo-Fabrizio fractional derivative appears in its non-singular kernel of a convolution type. The sufficient condition that guarantees a unique solution is obtained, the convergence of the series solution is discussed, and the maximum absolute error is estimated. Several numerical problems with an unknown exact solution are solved using the two techniques. A comparative study between the two solutions is presented. A comparative study shows that the time consumed by ADM is much smaller compared with the Picard technique.

Qualitative theory and approximate solution to a dynamical system under modified type Caputo-Fabrizio derivative

&lt;abstract&gt;&lt;p&gt;Qualitative theory, together with approximate solutions to a dynamic system, are investigated. The proposed mathematical model is composed of protected, susceptible, infected and treated classes. The adopted model expresses the mechanism of disease due to Typhoid fever. A modified type Caputo-Fabrizio fractional derivative (CFFD) is considered for the intended results. With the help of fixed point theory, some sufficient conditions for the existence of approximate solutions are developed. Also, to compute an approximate solution with respect to each compartment, we utilize the Laplace Transform and the Adomian decomposition method (ADM). A graphical presentation corresponding to some fundamental data is given.&lt;/p&gt;&lt;/abstract&gt;

MHD Flow of Second Grade Fluid with Heat Absorption and Chemical Reaction

The objective of this paper is to analyze the influence of thermo-diffusion on magnetohydrodynamics (MHD) flow of fractional second grade fluid immersed in a porous media over an exponentially accelerated vertical plate. In addition, other factors such as heat absorption and chemical reaction are used in the problem. More exactly, the fractional model has been developed using the generalized Fick’s and Fourier’s laws. The Caputo-Fabrizio (CF) fractional derivative has been used to solved the model. Initially, the flow modeled system of partial differential equations are transformed into dimensional form through suitable dimensionless variable and then Laplace transform technique has been used to solved the set of dimensionless governing equations for velocity profile, temperature profile, and concentration profile. The influence of different parameters like diffusion-thermo, fractional parameter, magnetic field, chemical reaction, heat obsorption, Schmidt number, time, Prandtl number and second grade parameter are discussed through numerous graphs. From figures, it is observed that fluid motion decreases with increasing values of Schmidt number, Prandtl number, magnetic parameter, and chemical reaction, whereas velocity field decreases with decreasing values of diffusion-thermo and mass grashof number. In order to check the athenticity of present work, we compare the present work with already published model graphically.