Caputo-Fabrizio Fractional Operator Research Articles

Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operator

يتم تطبيق تقنيات حساب التفاضل والتكامل الجزئي بنجاح في العديد من فروع العلوم والهندسة ، احدى هذه التقنيات طريقة تحليل الزكي وادوميان  (EADM) ، والتي لم يدرسها الباحثون باستخدام المشتق الكسري  لـ Caputo-Fabrizio. يهدف هذا العمل لدراسة طريقة تحليل الزكي وادوميان (EADM) لحل المعادلات التفاضلية الكسرية بمشتق Caputo-Fabrizio. قدمنا خوارزمية هذه الطريقة مع المؤثر CF وناقشنا تقاربها باستخدام طريقة سلسلة كوشي بعد ذلك ، تم تطبيق الطريقة لحل معادلات برجر، الشبية بالحرارة ، و برجر المزدوجة مع المؤثر Caputo -Fabrizio. في الختام أن الطريقة كانت متقاربة وفعالة لحل هذا النوع من المعادلات التفاضلية الكسرية.

On the dynamics of a nutrient–plankton system with Caputo and Caputo–Fabrizio fractional operators

This study aims to investigate the dynamics of a nutrient–plankton system by incorporating Caputo and Caputo–Fabrizio fractional operators. We examine the impact of fractional order on the stability of the nutrient–plankton interaction. The properties of the system’s solutions, such as the existence, uniqueness, and non-negativity under both operators, have been discussed. The system’s equilibria has been identified, and the conditions for their stability has been analyzed. The response of the system to fractional order through numerical simulations is visualized. It is observed that the system’s dynamics with the Caputo–Fabrizio fractional derivative are more similar to the system’s dynamics with integer order than with the Caputo fractional derivative.

A Study of Some New Hermite–Hadamard Inequalities via Specific Convex Functions with Applications

Convexity plays a crucial role in the development of fractional integral inequalities. Many fractional integral inequalities are derived based on convexity properties and techniques. These inequalities have several applications in different fields such as optimization, mathematical modeling and signal processing. The main goal of this article is to establish a novel and generalized identity for the Caputo–Fabrizio fractional operator. With the help of this specific developed identity, we derive new fractional integral inequalities via exponential convex functions. Furthermore, we give an application to some special means.

Fractional modeling and analysis of Hepatitis B virus using fixed-point approach

In this paper, we delve into the analysis of the Hepatitis B model, specifically the [Formula: see text] model, within the scope of the Caputo–Fabrizio fractional operator. A new state variable the number of vaccinated individuals is also added to the model. This addition enriches the scope of the hepatitis B model inviting a deeper exploration of the subject matter. Our study proves the existence of a disease-free fixed point within the proposed compartmental model. To ensure the existence and uniqueness of the fixed point, we employ a fixed-point result in the b-complete b-dislocated quasi-metric space, utilizing a Geraghty-type contraction mapping. This approach establishes the fixed point of a disease-free state within the model. Furthermore, we employ a two-step Adams–Bashforth numerical scheme, serving as a validation of both the significance of fractional-order derivatives and the validity of our obtained theoretical results. Together our research presents an innovative perspective on the [Formula: see text] hepatitis B model pushing the boundaries of understanding and shedding light on the dynamics of disease transmission with the impact of vaccine.

Numerical and graphical simulation of the non-linear fractional dynamical system of bone mineralization

<abstract><p>The objective of the present study was to improve our understanding of the complex biological process of bone mineralization by performing mathematical modeling with the Caputo-Fabrizio fractional operator. To obtain a better understanding of Komarova's bone mineralization process, we have thoroughly examined the boundedness, existence, and uniqueness of solutions and stability analysis within this framework. To determine how model parameters affect the behavior of the system, sensitivity analysis was carried out. Furthermore, the fractional Adams-Bashforth method has been used to carry out numerical and graphical simulations. Our work is significant owing to its comparison of fractional- and integer-order models, which provides novel insight into the effectiveness of fractional operators in representing the complex dynamics of bone mineralization.</p></abstract>

SOME NEW INTEGRAL INEQUALITIES VIA CAPUTO-FABRIZIO FRACTIONAL INTEGRAL OPERATOR

In this note, we have established some new integral inequalities
 for product of two integrable functions by using Young inequality with a wellknown
 classical inequality via Caputo-Fabrizio fractional integral operators.
 Then, we have given some special cases of the main findings. The main results
 have potential to usage in inequality theory.

New Estimations for Quasi-Convex Functions and \((h,m)\)-Convex Functions with the Help of Caputo-Fabrizio Fractional Integral Operators

The main motivation of the paper is to provide new integral inequalities for different kinds of convex functions by using a fractional integral operator with a non-singular kernel. The findings involve several new integral inequalities for quasi-convex functions and \((h,m)\)-convex functions. We have used the algebraic properties of Caputo-Fabrizio fractional operator, definitions of convex functions, and elementary analysis methods for the

On chaos control of nonlinear fractional Newton-Leipnik system via fractional Caputo-Fabrizio derivatives

In this work, we present a design for a Newton-Leipnik system with a fractional Caputo-Fabrizio derivative to explain its chaotic characteristics. This time-varying fractional Caputo-Fabrizio derivative approach is applied to solve the model numerically, and to check the solution’s existence and uniqueness. The existence and uniqueness of results of a fractional-order model under the Caputo-Fabrizio fractional operator have been proved by fixed point theory. As well, we achieved a stable result by applying the Ulam-Hyers concept. Chaos is controlled by linear controllers. Furthermore, the Lyapunov exponent of the system indicates that the chaos control findings are accurate. Based on weighted covariant Lyapunov vectors we construct a background covariance matrix using the Kaplan-Yorke dimension. Using a numerical example, this suggested method is illustrated for its applicability and efficiency.

Effect of Newtonian heating on double convection flow fractional differential type fluid

The influence of Newtonian heating (NH) is studied on heat-mass transfer problem of fractional differential type fluid. The proposed problem is modeled by using Caputo-Fabrizio fractional order derivative. A steady magnetic field of uniform strength is enforced in a perpendicular direction of flow. The set of governing equations in dimensional form accompanied by suitable initial and boundary conditions are changed into non-dimensional form by making use of some non-dimensional variables. The resulting problem is then converted into a model employing fractional differential operator by using the new Caputo-Fabrizio fractional differential operator. The analytical exact solution has been obtained by making use of Laplace transform technique. The numerical results are computed via MATHCAD software and displayed in various plots for different physical parameters and discussed.

Chaotic dynamics in a non-linear tumor-immune model with Caputo–Fabrizio fractional operator

Chaotic dynamics in a non-linear tumor-immune model with Caputo–Fabrizio fractional operator

Some New Fractional Hadamard and Pachpatte-Type Inequalities with Applications via Generalized Preinvexity

The term convexity associated with the theory of inequality in the sense of fractional analysis has a broad range of different and remarkable applications in the domain of applied sciences. The prime objective of this article is to investigate some new variants of Hermite–Hadamard and Pachpatte-type integral inequalities involving the idea of the preinvex function in the frame of a fractional integral operator, namely the Caputo–Fabrizio fractional operator. By employing our approach, a new fractional integral identity that correlates with preinvex functions for first-order differentiable mappings is presented. Moreover, we derive some refinements of the Hermite–Hadamard-type inequality for mappings, whose first-order derivatives are generalized preinvex functions in the Caputo–Fabrizio fractional sense. From an application viewpoint, to represent the usability of the concerning results, we presented several inequalities by using special means of real numbers. Integral inequalities in association with convexity in the frame of fractional calculus have a strong relationship with symmetry. Our investigation provides a better image of convex analysis in the frame of fractional calculus.

Impact of nanoparticles on vegetable oil as a cutting fluid with fractional ramped analysis

Better electrical insulation and thermal properties of vegetable oil with nanoparticles are crucial for its uses as a replacement for conventional previous lubricants used in heavy and light industries for cutting and machining. In this study, a magnetohydrodynamic (MHD) flow of a Brinkman-type nanofluid is used to investigate an infinite vertical plate with chemical reaction, heat radiation, and MHD flow. In order to improve the machining and cutting powers of regular vegetable oil, four distinct types of nanoparticles were selected to be the base fluid. The problem is modeled by coupled system partial differential equations (PDEs), and the results are generalized by the Caputo-Fabrizio fractional differential operator for the exponential non-singular kernel. In order to prepare nanofluids, four different types of nanoparticles, namely graphene oxide (GO), molybdenum disulfide (MoS2), titanium dioxide (TiO2), and aluminum oxide (Al2O3) are suspended separately in vegetable oil. The results of skin friction, the Nusselt number, and the Sherwood number are computed in various tables. It is found that GO nanoparticles, (followed by MoS2, TiO2, and Al2O3) are the materials that can heat transfer at the maximum rate. The heat transfer rate for GO is found to be the greatest with an enhancement up to 19.83% when 4% of nanoparticles are dispersed, followed by molybdenum disulfide at 16.96%, titanium dioxide at 16.25%, and alumina at 15.80%.

Modelling Influenza A disease dynamics under Caputo-Fabrizio fractional derivative with distinct contact rates

The objective of this manuscript is to present a novel approach to modeling influenza A disease dynamics by incorporating the Caputo-Fabrizio (CF) fractional derivative operator into the model. Particularly distinct contact rates between exposed and infected individuals are taken into account in the model under study, and the fractional derivative concept is explored with respect to this component. We demonstrate the existence and uniqueness of the solution and obtain the series solution for all compartments using the Laplace transform method. The reproduction number of the Influenza A model, which was created to show the effectiveness of different contact rates, was obtained and examined in detail in this sense. To validate our approach, we applied the predictor-corrector method in the sense of the Caputo-Fabrizio fractional derivative and demonstrate the effectiveness of the fractional derivative in accurately predicting disease dynamics. Our findings suggest that the use of the Caputo-Fabrizio fractional derivative can provide valuable insights into the mechanisms underlying influenza A disease and enhance the accuracy of disease models.

Some novel refinements of Hermite-Hadamard and Pachpatte type integral inequalities involving a generalized preinvex function pertaining to Caputo-Fabrizio fractional integral operator

<abstract><p>In this article, we aim to introduce and explore a new class of preinvex functions called $ \mathfrak{n} $-polynomial $ m $-preinvex functions, while also presenting algebraic properties to enhance their numerical significance. We investigate novel variations of Pachpatte and Hermite-Hadamard integral inequalities pertaining to the concept of preinvex functions within the framework of the Caputo-Fabrizio fractional integral operator. By utilizing this direction, we establish a novel fractional integral identity that relates to preinvex functions for differentiable mappings of first-order. Furthermore, we derive some novel refinements for Hermite-Hadamard type inequalities for functions whose first-order derivatives are polynomial preinvex in the Caputo-Fabrizio fractional sense. To demonstrate the practical utility of our findings, we present several inequalities using specific real number means. Overall, our investigation sheds light on convex analysis within the context of fractional calculus.</p></abstract>

New inequalities via Caputo-Fabrizio integral operator with applications

<abstract><p>Fractional integral inequalities have become one of the most useful and expansive tools for the development of many fields of pure and applied mathematics over the past few years. Many authors have just recently introduced various generalized inequalities that involved the fractional integral operators. The main goal of the present study is to incorporate the concept of strongly $ \left(s, m\right) $-convex functions and Hermite-Hadamard inequality with Caputo-Fabrizio integral operator. Also, we consider a new identity for twice differentiable mapping in the context of Caputo-Fabrizio fractional integral operator. Then, considering this identity as an auxiliary result, new mid-point version using well known inequalities like Hölder, power-mean, Young are presented. Moreover, some graphs of obtained inequalities are given for better understanding by the reader. Finally, we discussed some applications to matrix inequalities and spacial means.</p></abstract>

Dynamics of a fractional-order COVID-19 model under the nonsingular kernel of Caputo-Fabrizio operator

For the sake of human health, it is crucial to investigate infectious diseases including HIV/AIDS, hepatitis, and others. Worldwide, the recently discovered new coronavirus (COVID-19) poses a serious threat. The experimental vaccination and different COVID-19 strains found around the world make the virus' spread unavoidable. In the current research, fractional order is used to study the dynamics of a nonlinear modified COVID-19 SEIR model in the framework of the Caputo-Fabrizio fractional operator with order b. Fixed point theory has been used to investigate the qualitative analysis of the solution respectively. The well-known Laplace transform method is used to determine the approximate solution of the proposed model. Using the COVID-19 data that is currently available, numerical simulations are run to validate the necessary scheme and examine the dynamic behavior of the various compartments of the model. In order to stop the pandemic from spreading, our findings highlight the significance of taking preventative steps and changing one's lifestyle.

Analysis and dynamical transmission of Covid-19 model by using Caputo-Fabrizio derivative

The SARS-CoV-2 pandemic is an urgent problem with unpredictable properties and is widespread worldwide through human interactions. This work aims to use Caputo-Fabrizio fractional operators to explore the complex action of the Covid-19 Omicron variant. A fixed-point theorem and an iterative approach are used to prove the existence and singularity of the model’s system of solutions. Laplace transform is used to generalize the fractional order model for stability and unique solution of the iterative scheme. A numerical scheme is also constructed by using an exponential law kernel for the computational and simulation of the Covid-19 Model. The graphs demonstrate that the fractional model of Covid-19 is accurate. In the sense of Caputo-Fabrizio, one can obtain trustworthy information about the model in either an integer or non-integer scenario. This sense also provides useful information about the model’s complexity.

Free convection Hartmann flow of a viscous fluid with damped thermal transport through a cylindrical tube

• Free convection flow of viscous fluid in the presence of transverse magnetic field. • The thermal transport equation with Caputo-Fabrizio fractional integral operator. • The analytical solutions are found by using integral transforms. The free convection flow of a viscous fluid in a cylindrical tube is investigated in this article in the presence of a transverse magnetic field. The Caputo-Fabrizio fractional integral operator is used to generalize the thermal transport equation. Integral transforms, more specifically the Laplace and finite Hankel transforms, are used to find the solutions. The ordinary model is recovered as a particular case by taking the limit, and several more special instances are explored. Graphically, the impacts of the fractional and physical factors are highlighted. For a small and large values of time, the fractional parameter has distinct effects on the temperature and velocity.

New midpoint type Hermite-Hadamard-Mercer inequalities pertaining to Caputo-Fabrizio fractional operators

The objective of the current article is to incorporate the concepts of convexity and Jensen-Mercer inequality with the Caputo-Fabrizio fractional integral operator. Moreover, we present new midpoint versions of Hermite-Hadamard-Mercer (H-H-M) type inequalities for convex functions and the product of two convex functions on fractional integrals. Also, we consider a new identity for differentiable mappings in the context of the Caputo-Fabrizio fractional integral operators. Then, considering this identity as an auxiliary result, some new related H-H-M type inequality with the assistance of Hölder, power-mean, Young, and Hölder-İşcan inequality are presented. Finally, we give some applications of modified Bessel functions and matrices, and we also discuss some future scopes.

About Convergence and Order of Convergence of Some Fractional Derivatives

In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider some errors given by $\left|\left| D^{1-\al}f -f'\right|\right|_p$ for p=1 and $p=\infty$ and we prove that for both Caputo and Caputo Fabrizio operators the order of convergence is a positive real r, 0<r<1. Finally, we compare the speed of convergence between Caputo and Caputo-Fabrizio operators obtaining that they a related by the Digamma function.