Approximate Solution to the Fractional Lane–Emden Type Equations

Nouh, M. I.; Abdel-Salam, Emad A.-B.

doi:10.1007/s40995-017-0246-5

Cited by 11 publications

(2 citation statements)

References 46 publications

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“…Nowadays, generalizations of some of the basic differential equations in physics led to new and more deep insight to the macroscopic phenomena in a wide range of areas like anomalous diffusion, signal processing and quantum mechanics (Podlubny 1999;Sokolov et al 2002;Kilbas et al 2006;Laskin 2000). In astrophysics, El-Nabulsi (2011) considered a fractional equation of state for white dwarf stars; Bayian and Krisch (2015) have investigated the fractional versions of the stellar structure equations for non-radiating spherical objects, Abdel-Salam and Nouh (2016) and Nouh and Abdel-Salam (2017) introduced a series solution to the fractional isothermal and polytropic gas spheres and obtained a solution converges to the surface of the sphere with a few series terms when compared with the solution of the integer one.…”

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confidence: 99%

Computational method for a fractional model of the helium burning network

Nouh

2019

New Astronomy

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Stellar cores may be considered as a nuclear reactor that play important role in injecting new synthesized elements in the interstellar medium Helium burning is an important stage that contribute to the synthesis of key elements such as carbon, through the triple-α process, and oxygen. In the present paper, we introduce a computational method for the fractional model of the nuclear helium burning in stellar cores. The system of fractional differential equations is solved simultaneously using series expansion method. The calculations are performed in the sense of modified Riemann-Liouville fractional derivative. Analytic expressions are obtained for the abundance of each element as a function of time. Comparing the abundances calculated at the fractional parameter 1   , which represents the integer solution, with the numerical solution revealed a good agreement with maximum error 0.003   . The product abundances are calculated at 0.25, 0.5, 0.75   to declare the effects of changing the fractional parameters on the calculations.

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Computational method for a fractional model of the helium burning network

Nouh

2019

New Astronomy

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“…Abdel-Salam and Yousif [22] discussed solving the nonlinear space-time fractional differential equations by the fractional Riccati expansion approach. The approximate solution to the fractional Lane-Emden kind equations was studied by Nouh and Abdel-Salam [23]. Examining the fractional derivative for natural convection in a slanted cavity having porous media was discussed by Ahmed et al [24].…”

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confidence: 99%

Noninteger Derivative Order Analysis on Plane Wave Reflection from Electro-Magneto-Thermo-Microstretch Medium with a Gravity Field within the Three-Phase Lag Model

Elhag

Bayones

Kilany

et al. 2022

Advances in Mathematical Physics

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The present research paper illustrates how noninteger derivative order analysis affects the reflection of partial thermal expansion waves under the generalized theory of plane harmonic wave reflection from a semivacuum elastic solid material with both gravity and magnetic field in the three-phase lag model (3PHL). The main goal for this study is investigating the fractional order impact and the applications related to the orders, especially in biology, medicine, and bioinformatics, besides the integer order considering an external effect, such as electromagnetic, gravity, and phase lags in a microstretch medium. The problem fractional form was formulated, and the boundary conditions were applied. The results were displayed graphically, considering the 3PHL model with magnetic field, gravity, and relaxation time. These findings were an explicit comparison of the effect of the plane wave reflection amplitude with integer derivative order analysis and noninteger derivative order analysis. The fractional order was compared to the correspondence integer order that indicated to the difference between them and agreement with the applications in biology, medicine, and other related topics. This phenomenon has more applications in relation to the biology and biomathematics problems.

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Analytical Solutions of a Class of Fractional Lane–Emden Equation: A Power Series Method

Awonusika

2022

Int. J. Appl. Comput. Math

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Approximate Solution to the Fractional Lane–Emden Type Equations

Cited by 11 publications

References 46 publications

Computational method for a fractional model of the helium burning network

Computational method for a fractional model of the helium burning network

Noninteger Derivative Order Analysis on Plane Wave Reflection from Electro-Magneto-Thermo-Microstretch Medium with a Gravity Field within the Three-Phase Lag Model

Analytical Solutions of a Class of Fractional Lane–Emden Equation: A Power Series Method

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