1,721,540 research outputs found
Properties of the Caputo-Fabrizio Fractional Derivative
Full text linkIn this paper, we investigate some properties related Caputo-Fabrizio (CF) fractional derivative. We prove some regularity properties and bounds characterizing the Caputo-Fabrizio derivative operator. Using the method of Laplace transform, we found explicit solutions of some differential equations containing the Caputo-Fabrizio fractional derivative. Different types of inequalities generated by using the Caputo-Fabrizio derivative are also presented
Application of caputo–fabrizio operator to suppress the aedes aegypti mosquitoes via wolbachia: an LMI approach
Full text linkThe aim of this paper is to establish the stability results based on the approach of Linear Matrix Inequality (LMI) for the addressed mathematical model using Caputo–Fabrizio operator (CF operator). Firstly, we extend some existing results of Caputo fractional derivative in the literature to a new fractional order operator without using singular kernel which was introduced by Caputo and Fabrizio. Secondly, we have created a mathematical model to increase Cytoplasmic Incompatibility (CI) in Aedes Aegypti mosquitoes by releasing Wolbachia infected mosquitoes. By this, we can suppress the population density of A.Aegypti mosquitoes and can control most common mosquito-borne diseases such as Dengue, Zika fever, Chikungunya, Yellow fever and so on. Our main aim in this paper is to examine the behaviours of Caputo–Fabrizio operator over the logistic growth equation of a population system then, prove the existence and uniqueness of the solution for the considered mathematical model using CF operator. Also, we check the alpha-exponential stability results for the system via linear matrix inequality technique. Finally a numerical example is provided to check the behaviour of the CF operator on the population system by incorporating the real world data available in the known literature
On Discrete Delta Caputo–Fabrizio Fractional Operators and Monotonicity Analysis
No full textThe discrete delta Caputo-Fabrizio fractional differences and sums are proposed to distinguish their monotonicity analysis from the sense of Riemann and Caputo operators on the time scale Z. Moreover, the action of Q− operator and discrete delta Laplace transform method are also reported. Furthermore, a relationship between the discrete delta Caputo-Fabrizio-Caputo and Caputo-Fabrizio-Riemann fractional differences is also studied in detail. To better understand the dynamic behavior of the obtained monotonicity results, the fractional difference mean value theorem is derived. The idea used in this article is readily applicable to obtain monotonicity analysis of other discrete fractional operators in discrete fractional calculus
On Some Fractional Integral Inequalities Involving Caputo–Fabrizio Integral Operator
No full textIn this paper, we deal with the Caputo–Fabrizio fractional integral operator with a nonsingular kernel and establish some new integral inequalities for the Chebyshev functional in the case of synchronous function by employing the fractional integral. Moreover, several fractional integral inequalities for extended Chebyshev functional by considering the Caputo–Fabrizio fractional integral operator are discussed. In addition, we obtain fractional integral inequalities for three positive functions involving the same operator
On the existence of solutions for some infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential equations
No full textAbstract By mixing the idea of 2-arrays, continued fractions, and Caputo-Fabrizio fractional derivative, we introduce a new operator entitled the infinite coefficient-symmetric Caputo-Fabrizio fractional derivative. We investigate the approximate solutions for two infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential problems. Finally, we analyze two examples to confirm our main results
Caputo Fabrizio Bézier Curve with Fractional and Shape Parameters
No full textIn recent research in computer-aided geometric design (CAGD), one of the most popular concerns has been the creation of new basis functions for the Bézier curve. Bézier curves with high degrees often overshoot, which makes it challenging to maintain control over the ideal length of the curved trajectory. To get around this restriction, free-form surfaces and curves can be created using the Caputo Fabrizio basis function. In this study, the Caputo Fabrizio fractional order derivative is used to construct the Caputo Fabrizio basis function, which contains fractional parameter and shape parameters. The Caputo Fabrizio Bézier curve and surface are defined using the Caputo Fabrizio basis function, and their geometric properties are examined. Using fractional and shape parameters in the implementation of the Caputo Fabrizio basis function offers an alternative perspective on how the Caputo Fabrizio basis function can construct complicated curves and surfaces beyond a limited formulation. Curves and surfaces can have additional shape and length control by adjusting a number of fractional and shape parameters without affecting their control points. The Caputo Fabrizio Bézier curve’s flexibility and versatility make it more effective in creating complex engineering curves and surfaces
A new study on the Newell-Whitehead-Segel equation with Caputo-Fabrizio fractional derivative
No full textIn this research, we propose a new numerical method that combines with the Caputo-Fabrizio Elzaki transform and the q-homotopy analysis transform method. This work aims to analyze the Caputo-Fabrizio fractional Newell-Whitehead-Segel (NWS) equation utilizing the Caputo-Fabrizio q-Elzaki homotopy analysis transform method. The Newell-Whitehead-Segel equation is a partial differential equation employed for modeling the dynamics of reaction-diffusion systems, specifically in the realm of pattern generation in biological and chemical systems. A convergence analysis of the proposed method was performed. Two-dimensional and three-dimensional graphs of the solutions have been drawn with the Maple software. It is seen that the resulting proposed method is more powerful and effective than the Aboodh transform homotopy perturbation method and conformable Laplace decomposition method in the results. © 2024 the Author(s), licensee AIMS Press
Caputo-Fabrizio approach to numerical fractional derivatives
Full text linkFractional calculus is an essential tool in every area of science today. This work gives the quadratic interpolation-based L1-2 formula for the Caputo-Fabrizio derivative, a numerical technique for approximating the fractional derivative. To get quadratic and cubic convergence rates, respectively, we study the use of Lagrange interpolation in the L1 and L1-2 formulations. Our numerical analysis shows the accuracy of the theory’s predicted convergence rates. The L1-2 formula aims to enhance the accuracy and usability of a flexible tool for many applications in science and mathematics. We demonstrate the validity of the theory’s predicted convergence rates using numerical analysis. Several numerical examples are also given to show how the suggested approaches may be utilized to determine the Caputo-Fabrizio derivative of well-known functions. Lagrange interpolation is used in the L1 and L1-2 procedures to obtain quadratic and cubic convergence rates, respectively. The numerical study demonstrates that the L1-2 formula offers greater accuracy when compared to current approaches. In addition, it is a better apparatus for several applications in science and mathematics. Due to its higher convergence rate, the L1-2 formula outperforms other available numerical methods for scientific computations. The L1-2 formula, a novel numerical method for the Caputo-Fabrizio derivative that makes use of quadratic interpolation, is introduced in this study as a conclusion
Caputo-Fabrizio approach to numerical fractional derivatives
Full text linkFractional calculus is an essential tool in every area of science today. This work gives the quadratic interpolation-based L1-2 formula for the Caputo-Fabrizio derivative, a numerical technique for approximating the fractional derivative. To get quadratic and cubic convergence rates, respectively, we study the use of Lagrange interpolation in the L1 and L1-2 formulations. Our numerical analysis shows the accuracy of the theory’s predicted convergence rates. The L1-2 formula aims to enhance the accuracy and usability of a flexible tool for many applications in science and mathematics. We demonstrate the validity of the theory’s predicted convergence rates using numerical analysis. Several numerical examples are also given to show how the suggested approaches may be utilized to determine the Caputo-Fabrizio derivative of well-known functions. Lagrange interpolation is used in the L1 and L1-2 procedures to obtain quadratic and cubic convergence rates, respectively. The numerical study demonstrates that the L1-2 formula offers greater accuracy when compared to current approaches. In addition, it is a better apparatus for several applications in science and mathematics. Due to its higher convergence rate, the L1-2 formula outperforms other available numerical methods for scientific computations. The L1-2 formula, a novel numerical method for the Caputo-Fabrizio derivative that makes use of quadratic interpolation, is introduced in this study as a conclusion
A new numerical solution of the competition model among bank data in Caputo-Fabrizio derivative
Full text linkA new numerical scheme for the Caputo-Fabrizio operator is proposed. We initially present a bank model with real data and then present the model in the fractional Caputo-Fabrizio derivative. We estimate and fit the model parameter using the least square curve fitting. The Caputo-Fabrizio model is solved numerically by using three steps Adams-Bashforth method. The proposed scheme is used to obtain graphical results for bank data of rural and commercial. The real data of rural and commercial banks are used to fit with Caputo-Fabrizio model. We show that the Caputo-Fabrizio model show good fitting for the fractional order parameters versus the real data of rural and commercial bank. Further, we show graphical illustration for some values of the fractional order in order to show the effectiveness of the proposed new numerical scheme
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