The Experts below are selected from a list of 2364 Experts worldwide ranked by ideXlab platform
Hossein Jafari - One of the best experts on this subject based on the ideXlab platform.
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solving a multi order fractional differential equation using homotopy analysis method
Journal of King Saud University - Science, 2011Co-Authors: Hossein Jafari, S Das, Haleh TajadodiAbstract:Abstract In this paper we have used the homotopy analysis method (HAM) to obtain solution of multi-order fractional differential equation. The fractional derivative is described in the Caputo Sense. Some illustrative examples have been presented.
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homotopy analysis method for solving multi term linear and nonlinear diffusion wave equations of fractional order
Computers & Mathematics With Applications, 2010Co-Authors: Hossein Jafari, A Golbabai, S Seifi, Khosro SayevandAbstract:Abstract In this paper we have used the homotopy analysis method (HAM) to obtain solutions of multi-term linear and nonlinear diffusion–wave equations of fractional order. The fractional derivative is described in the Caputo Sense. Some illustrative examples have been presented.
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solving a system of nonlinear fractional partial differential equations using homotopy analysis method
Communications in Nonlinear Science and Numerical Simulation, 2009Co-Authors: Hossein Jafari, S SeifiAbstract:Abstract In this article, the homotopy analysis method (HAM) has been employed to obtain solutions of a System of nonlinear fractional partial differential equations. This indicates the validity and great potential of the homotopy analysis method for solving system of fractional partial differential equations. The fractional derivative is described in the Caputo Sense.
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homotopy analysis method for solving linear and nonlinear fractional diffusion wave equation
Communications in Nonlinear Science and Numerical Simulation, 2009Co-Authors: Hossein Jafari, S SeifiAbstract:Abstract In this paper, we adopt the homotopy analysis method (HAM) to obtain solutions of linear and nonlinear fractional diffusion and wave equation. The fractional derivative is described in the Caputo Sense. Some illustrative examples are presented.
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solving a fourth order fractional diffusion wave equation in a bounded domain by decomposition method
Numerical Methods for Partial Differential Equations, 2008Co-Authors: Hossein Jafari, Mehdi Dehghan, Khosro SayevandAbstract:In this article, the Adomian decomposition method has been used to obtain solutions of fourth-order fractional diffusion-wave equation defined in a bounded space domain. The fractional derivative is described in the Caputo Sense. Convergence of the method has been discussed with some illustrative examples. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008
Sania Qureshi - One of the best experts on this subject based on the ideXlab platform.
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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...
Asif Ali Shaikh - One of the best experts on this subject based on the ideXlab platform.
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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...
S Seifi - One of the best experts on this subject based on the ideXlab platform.
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homotopy analysis method for solving multi term linear and nonlinear diffusion wave equations of fractional order
Computers & Mathematics With Applications, 2010Co-Authors: Hossein Jafari, A Golbabai, S Seifi, Khosro SayevandAbstract:Abstract In this paper we have used the homotopy analysis method (HAM) to obtain solutions of multi-term linear and nonlinear diffusion–wave equations of fractional order. The fractional derivative is described in the Caputo Sense. Some illustrative examples have been presented.
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solving a system of nonlinear fractional partial differential equations using homotopy analysis method
Communications in Nonlinear Science and Numerical Simulation, 2009Co-Authors: Hossein Jafari, S SeifiAbstract:Abstract In this article, the homotopy analysis method (HAM) has been employed to obtain solutions of a System of nonlinear fractional partial differential equations. This indicates the validity and great potential of the homotopy analysis method for solving system of fractional partial differential equations. The fractional derivative is described in the Caputo Sense.
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homotopy analysis method for solving linear and nonlinear fractional diffusion wave equation
Communications in Nonlinear Science and Numerical Simulation, 2009Co-Authors: Hossein Jafari, S SeifiAbstract:Abstract In this paper, we adopt the homotopy analysis method (HAM) to obtain solutions of linear and nonlinear fractional diffusion and wave equation. The fractional derivative is described in the Caputo Sense. Some illustrative examples are presented.
Shaher Momani - One of the best experts on this subject based on the ideXlab platform.
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analytical approximate solutions of the fractional convection diffusion equation with nonlinear source term by he s homotopy perturbation method
International Journal of Computer Mathematics, 2010Co-Authors: Shaher Momani, Ahmet YildirimAbstract:In this study, we present a framework to obtain analytical approximate solutions to the nonlinear fractional convection-diffusion equation. The fractional derivative is considered in the Caputo Sense. The applications of the homotopy perturbation method were extended to derive analytical solutions in the form of a series with easily computed terms for this equation. Some examples are tested and the results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations of fractional order.
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solving fractional diffusion and wave equations by modified homotopy perturbation method
Physics Letters A, 2007Co-Authors: Hossein Jafari, Shaher MomaniAbstract:This Letter applies the modified He's homotopy perturbation method (HPM) suggested by Momani and Odibat to obtaining solutions of linear and nonlinear fractional diffusion and wave equations. The fractional derivative is described in the Caputo Sense. Some illustrative examples are given, revealing the effectiveness and convenience of the method.
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comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
Computers & Mathematics With Applications, 2007Co-Authors: Shaher Momani, Zaid OdibatAbstract:In this article, the homotopy perturbation method proposed by J.- H. He is adopted for solving linear fractional partial differential equations. The fractional derivatives are described in the Caputo Sense. Comparison of the results obtained by the homotopy perturbation method with those obtained by the variational iteration method reveals that the present methods are very effective and convenient.
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numerical approximations and pade approximants for a fractional population growth model
Applied Mathematical Modelling, 2007Co-Authors: Shaher Momani, Rami QarallehAbstract:Abstract This paper presents an efficient numerical algorithm for approximate solutions of a fractional population growth model in a closed system. The time-fractional derivative is considered in the Caputo Sense. The algorithm is based on Adomian’s decomposition approach and the solutions are calculated in the form of a convergent series with easily computable components. Then the Pade approximants are effectively used in the analysis to capture the essential behavior of the population u(t) of identical individuals.
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homotopy perturbation method for nonlinear partial differential equations of fractional order
Physics Letters A, 2007Co-Authors: Shaher Momani, Zaid OdibatAbstract:The aim of this Letter is to present an efficient and reliable treatment of the homotopy perturbation method (HPM) for nonlinear partial differential equations with fractional time derivative. The fractional derivative is described in the Caputo Sense. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.
