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Sania Qureshi - One of the best experts on this subject based on the ideXlab platform.
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Fractional modeling of blood ethanol concentration system with real data application
Chaos, 2019Co-Authors: Sania Qureshi, Abdullahi Yusuf, Asif Ali Shaikh, Dumitru BaleanuAbstract:In this study, a physical system called the blood ethanol concentration model has been investigated in its Fractional (non-integer) order version. The three most commonly used Fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu Fractional Derivative in the Caputo sense—ABC and the Caputo-Fabrizio—CF) kernels have been used to Fractionalize the model, whereas during the process of Fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the Fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of squared residuals is carried out to show the performance of the models along with some graphical illustrations.In this study, a physical system called the blood ethanol concentration model has been investigated in its Fractional (non-integer) order version. The three most commonly used Fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu Fractional Derivative in the Caputo sense—ABC and the Caputo-Fabrizio—CF) kernels have been used to Fractionalize the model, whereas during the process of Fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the Fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of sq...
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two strain epidemic model involving Fractional Derivative with mittag leffler kernel
Chaos, 2018Co-Authors: Abdullahi Yusuf, Dumitru Baleanu, Sania Qureshi, Aliyu Isa Aliyu, Asif Ali ShaikhAbstract:In the present study, the Fractional version with respect to the Atangana-Baleanu Fractional Derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving tw...
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two strain epidemic model involving Fractional Derivative with mittag leffler kernel
Chaos, 2018Co-Authors: Abdullahi Yusuf, Dumitru Baleanu, Sania Qureshi, Aliyu Isa Aliyu, Asif Ali ShaikhAbstract:In the present study, the Fractional version with respect to the Atangana-Baleanu Fractional Derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed Fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its Fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu Fractional Derivative operator in the caputo sense. To believe upon the results obtained, the Fractional order α has been allowed to vary between ( 0 , 1 ] , whereupon the physical observations match with those obtained in the classical case, but the Fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of Fractional order Derivatives for ABC. Finally, the Fractional forward Euler method in the classical caputo sense has been used to illustrate the better performance of the numerical method obtained via the Atangana-Baleanu Fractional Derivative operator in the caputo sense.In the present study, the Fractional version with respect to the Atangana-Baleanu Fractional Derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed Fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its Fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu Fractional Derivative operator in the caputo sense. To believe upon the results obtained, the Fractional...
Dumitru Baleanu - One of the best experts on this subject based on the ideXlab platform.
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numerical solutions of the Fractional fisher s type equations with atangana Baleanu Fractional Derivative by using spectral collocation methods
Chaos, 2019Co-Authors: Khaled M Saad, J F Gomezaguilar, M M Khader, Dumitru BaleanuAbstract:The main objective of this paper is to investigate an accurate numerical method for solving a biological Fractional model via Atangana-Baleanu Fractional Derivative. We focused our attention on linear and nonlinear Fisher’s equations. We use the spectral collocation method based on the Chebyshev approximations. This method reduced the nonlinear equations to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them by using the finite difference method. This is the first time that this method is used to solve nonlinear equations in Atangana-Baleanu sense. We present the effectiveness and accuracy of the proposed method by computing the absolute error and the residual error functions. The results show that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.
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Fractional modeling of blood ethanol concentration system with real data application
Chaos, 2019Co-Authors: Sania Qureshi, Abdullahi Yusuf, Asif Ali Shaikh, Dumitru BaleanuAbstract:In this study, a physical system called the blood ethanol concentration model has been investigated in its Fractional (non-integer) order version. The three most commonly used Fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu Fractional Derivative in the Caputo sense—ABC and the Caputo-Fabrizio—CF) kernels have been used to Fractionalize the model, whereas during the process of Fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the Fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of squared residuals is carried out to show the performance of the models along with some graphical illustrations.In this study, a physical system called the blood ethanol concentration model has been investigated in its Fractional (non-integer) order version. The three most commonly used Fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu Fractional Derivative in the Caputo sense—ABC and the Caputo-Fabrizio—CF) kernels have been used to Fractionalize the model, whereas during the process of Fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the Fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of sq...
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two strain epidemic model involving Fractional Derivative with mittag leffler kernel
Chaos, 2018Co-Authors: Abdullahi Yusuf, Dumitru Baleanu, Sania Qureshi, Aliyu Isa Aliyu, Asif Ali ShaikhAbstract:In the present study, the Fractional version with respect to the Atangana-Baleanu Fractional Derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving tw...
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two strain epidemic model involving Fractional Derivative with mittag leffler kernel
Chaos, 2018Co-Authors: Abdullahi Yusuf, Dumitru Baleanu, Sania Qureshi, Aliyu Isa Aliyu, Asif Ali ShaikhAbstract:In the present study, the Fractional version with respect to the Atangana-Baleanu Fractional Derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed Fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its Fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu Fractional Derivative operator in the caputo sense. To believe upon the results obtained, the Fractional order α has been allowed to vary between ( 0 , 1 ] , whereupon the physical observations match with those obtained in the classical case, but the Fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of Fractional order Derivatives for ABC. Finally, the Fractional forward Euler method in the classical caputo sense has been used to illustrate the better performance of the numerical method obtained via the Atangana-Baleanu Fractional Derivative operator in the caputo sense.In the present study, the Fractional version with respect to the Atangana-Baleanu Fractional Derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed Fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its Fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu Fractional Derivative operator in the caputo sense. To believe upon the results obtained, the Fractional...
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analysis of regularized long wave equation associated with a new Fractional operator with mittag leffler type kernel
Physica A-statistical Mechanics and Its Applications, 2018Co-Authors: Devendra Kumar, Jagdev Singh, Dumitru BaleanuAbstract:Abstract In this work, we aim to present a new Fractional extension of regularized long-wave equation. The regularized long-wave equation is a very important mathematical model in physical sciences, which unfolds the nature of shallow water waves and ion acoustic plasma waves. The existence and uniqueness of the solution of the regularized long-wave equation associated with Atangana–Baleanu Fractional Derivative having Mittag-Leffler type kernel is verified by implementing the fixed-point theorem. The numerical results are derived with the help of an iterative algorithm. In order to show the effects of various parameters and variables on the displacement, the numerical results are presented in graphical and tabular form.
Behzad Ghanbari - One of the best experts on this subject based on the ideXlab platform.
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fuzzy Fractional differential equations with the generalized atangana Baleanu Fractional Derivative
Fuzzy Sets and Systems, 2020Co-Authors: Behzad Ghanbari, Ngo Van HoaAbstract:Abstract In this paper, we introduce a generalization of Atangana-Baleanu type Fractional calculus with respect to the generalized Mittag-Leffler kernel which has been named as the generalized Atangana-Baleanu (GAB) type Fractional calculus. Existence and uniqueness results for the initial value problems of fuzzy differential equations involving a GAB Fractional Derivative in the Caputo sense are established by employing the method of successive approximation and by means of fixed point theorems. To visualize the theoretical results, some examples and numerical simulations are given.
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on approximate solutions for a Fractional prey predator model involving the atangana Baleanu Derivative
Advances in Difference Equations, 2020Co-Authors: Behzad GhanbariAbstract:Mathematical modeling has always been one of the most potent tools in predicting the behavior of dynamic systems in biology. In this regard, we aim to study a three-species prey–predator model in the context of Fractional operator. The model includes two competing species with logistic growing. It is considered that one of the competitors is being predated by the third group with Holling type II functional response. Moreover, one another competitor is in a commensal relationship with the third category acting as its host. In this model, the Atangana–Baleanu Fractional Derivative is used to describe the rate of evolution of functions in the model. Using a creative numerical trick, an iterative method for determining the numerical solution of Fractional systems has been developed. This method provides an implicit form for determining solution approximations that can be solved by standard methods in solving nonlinear systems such as Newton’s method. Using this numerical technique, approximate answers for this system are provided, assuming several categories of possible choices for the model parameters. In the continuation of the simulations, the sensitivity analysis of the solutions to some parameters is examined. Some other theoretical features related to the model, such as expressing the necessary conditions on the stability of equilibrium points as well as the existence and uniqueness of solutions, are also examined in this article. It is found that utilizing the concept of Fractional Derivative order the flexibility of the model in justifying different situations for the system has increased. The use of Fractional operators in the study of other models in computational biology is recommended.
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an application of the atangana Baleanu Fractional Derivative in mathematical biology a three species predator prey model
Chaos Solitons & Fractals, 2020Co-Authors: Behzad Ghanbari, H M Srivastava, Hatira GunerhanAbstract:Abstract In recent decades, studying the behavior of biological species has become one of the most fascinating areas of applied mathematics. The high importance of conservation of rare species in nature has prompted researchers in various fields to pay particular attention to this issue. Therefore, it is essential to develop mathematical models that examine the dynamics of their behavior. On the other hand, the development of new concepts in numerical analysis has enabled us to preserve more information on the evolutionary behavior history of a dynamic system and to use it in predicting the new features of the system. Fractional Derivatives have provided such a valuable tool. This paper studies a dynamic system that models the interactions between two densities of immature and mature prey and predator populations. In the model, prey population is divided into two populations, including mature prey and immature prey. Another feature of the model is that predator depends on mature prey only and it followed by Crowley-Martin type functional response. Moreover, the Fractional operator used in this model as Derivative is of the Atangana-Baleanu AB type. Using this kind of Fractional Derivative causes the results to depend on the Fractional order of the Derivative. The addition of the concept of memory to the model is another highlight of using this type of Derivative for the biological model. This helps the model to apply all the essential information of the phenomenon from the beginning to the desired time in the calculations. Existence and uniqueness of solutions to the Fractional model are also investigated in this manuscript. The numerical method used in the article is also one of the most efficient patterns in solving problems with Fractional Derivatives. Using this effective method makes the results very consistent with what we actually expect to happen. Many simulations have been carried out to investigate the effect of parameters in the model on its overall behavior. Numerical results show the impressive performance of the Fractional operator on the dynamic behavior of the considered predator-prey model. This efficient Fractional operator can also be tested in the structure of other existing biological models.
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on the fuzzy Fractional differential equation with interval atangana Baleanu Fractional Derivative approach
Chaos Solitons & Fractals, 2020Co-Authors: T Allahviranloo, Behzad GhanbariAbstract:Abstract The fuzzy systems with interval approach use an infinite valued parameter in the range of [0,1] as a confidence degree of belief. This parameter makes more complicity but plays the main role in creating the fuzzy solution of the fuzzy systems. In solving process of the model, the Atangana–Baleanu Derivative in the Fractional case of differential equations has a memory to use all the previous information. Therefore this is as a key point and advantage of using this Derivative to reduce the complicity of numerical results in comparison with other known Derivatives. In this paper, first, the ABC Fractional Derivative on fuzzy set-valued functions in parametric interval form is defined. Then it is applied for proving the existence and uniqueness of the solution of fuzzy Fractional differential equation with ABC Fractional Derivative. In general, it is shown that the last interval model is as a coupled system of nonlinear equations. To solve the final system an efficient numerical method called ABC-PI is used. For more illustration, several examples are solved numerically and analyzed by the figures.
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new numerical simulations for some real world problems with atangana Baleanu Fractional Derivative
Chaos Solitons & Fractals, 2019Co-Authors: Wei Gao, Behzad Ghanbari, Haci Mehmet BaskonusAbstract:Abstract In this work, we introduce ABC-Caputo operator with ML kernel and its main characteristics are discussed. Viral diseases models for AIDS and Zika are considered, and finally, as third model, the macroeconomic model involving ABC Fractional Derivatives is investigated, respectively. It is presented that the AB Caputo Derivatives satisfy the Lipschitz condition along with superposition property. The numerical methods for solving the Fractional models are presented by means of ABC Fractional Derivative in a detailed manner. Finally the simulation results obtained in this paper according to the suitable values of parameters are also manifested.
Asif Ali Shaikh - One of the best experts on this subject based on the ideXlab platform.
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Fractional modeling of blood ethanol concentration system with real data application
Chaos, 2019Co-Authors: Sania Qureshi, Abdullahi Yusuf, Asif Ali Shaikh, Dumitru BaleanuAbstract:In this study, a physical system called the blood ethanol concentration model has been investigated in its Fractional (non-integer) order version. The three most commonly used Fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu Fractional Derivative in the Caputo sense—ABC and the Caputo-Fabrizio—CF) kernels have been used to Fractionalize the model, whereas during the process of Fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the Fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of squared residuals is carried out to show the performance of the models along with some graphical illustrations.In this study, a physical system called the blood ethanol concentration model has been investigated in its Fractional (non-integer) order version. The three most commonly used Fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu Fractional Derivative in the Caputo sense—ABC and the Caputo-Fabrizio—CF) kernels have been used to Fractionalize the model, whereas during the process of Fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the Fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of sq...
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two strain epidemic model involving Fractional Derivative with mittag leffler kernel
Chaos, 2018Co-Authors: Abdullahi Yusuf, Dumitru Baleanu, Sania Qureshi, Aliyu Isa Aliyu, Asif Ali ShaikhAbstract:In the present study, the Fractional version with respect to the Atangana-Baleanu Fractional Derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving tw...
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two strain epidemic model involving Fractional Derivative with mittag leffler kernel
Chaos, 2018Co-Authors: Abdullahi Yusuf, Dumitru Baleanu, Sania Qureshi, Aliyu Isa Aliyu, Asif Ali ShaikhAbstract:In the present study, the Fractional version with respect to the Atangana-Baleanu Fractional Derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed Fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its Fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu Fractional Derivative operator in the caputo sense. To believe upon the results obtained, the Fractional order α has been allowed to vary between ( 0 , 1 ] , whereupon the physical observations match with those obtained in the classical case, but the Fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of Fractional order Derivatives for ABC. Finally, the Fractional forward Euler method in the classical caputo sense has been used to illustrate the better performance of the numerical method obtained via the Atangana-Baleanu Fractional Derivative operator in the caputo sense.In the present study, the Fractional version with respect to the Atangana-Baleanu Fractional Derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed Fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its Fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu Fractional Derivative operator in the caputo sense. To believe upon the results obtained, the Fractional...
Khaled M Saad - One of the best experts on this subject based on the ideXlab platform.
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an efficient semi analytical method for solving the generalized regularized long wave equations with a new Fractional Derivative operator
Journal of King Saud University - Science, 2021Co-Authors: H M Srivastava, Sinan Deniz, Khaled M SaadAbstract:Abstract In this work, the newly developed optimal perturbation iteration technique with Laplace transform is applied to the generalized regularized long wave equations with a new Fractional operator to obtain new approximate solutions. We transform the classical generalized regularized long wave equations to Fractional differential form by using the Atangana-Baleanu Fractional Derivative which is defined with the Mittag-Leffler function. To show the efficiency of the proposed method, a numerical example is given for different values of physical parameters.
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numerical solutions of the Fractional fisher s type equations with atangana Baleanu Fractional Derivative by using spectral collocation methods
Chaos, 2019Co-Authors: Khaled M Saad, J F Gomezaguilar, M M Khader, Dumitru BaleanuAbstract:The main objective of this paper is to investigate an accurate numerical method for solving a biological Fractional model via Atangana-Baleanu Fractional Derivative. We focused our attention on linear and nonlinear Fisher’s equations. We use the spectral collocation method based on the Chebyshev approximations. This method reduced the nonlinear equations to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them by using the finite difference method. This is the first time that this method is used to solve nonlinear equations in Atangana-Baleanu sense. We present the effectiveness and accuracy of the proposed method by computing the absolute error and the residual error functions. The results show that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.
