Fractional Differential Equations

Numerical Initial Value Problems in Ordinary Differential Equations

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

This paper points out the fractional complex transform method for wave equations on Cantor sets within the local differential fractional operators. The proposed method is efficient to handle differential equations on Cantor sets.

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Fractional complex transform method for wave equations on Cantor sets within local fractional differential operator

This article is interested in presenting and implementing two new numerical algorithms for solving multi-term fractional differential equations. The idea behind the proposed algorithms is based on establishing a novel operational matrix of fractional-order differentiation of generalized Lucas polynomials in the Caputo sense. This operational matrix serves as a powerful tool for obtaining the desired numerical solutions. The resulting solutions are spectral, and they are built on utilizing tau and collocation methods. A new treatment of convergence and error analysis of the suggested generalized Lucas expansion is presented. The presented numerical results demonstrate the efficiency, applicability and high accuracy of the proposed algorithms.

Generalized Lucas polynomial sequence approach for fractional differential equations

Numerical solutions of fuzzy differential equations by extended Runge--Kutta-like formulae of order 4

The Adomian decomposition method is proposed to solve fractional Bratu-type equations. The iteration procedure is based on a fractional Taylor series. Three examples are illustrated to show the presented method’s efficiency and convenience.

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Adomian Decomposition Method for Solving Fractional Bratu-type Equations

https://lu.ac.ir/usersfiles/889215360-HAMFNE.pdf

Homotopy analysis method for the fractional nonlinear equations

/pdf/solving-system-of-fractional-differential-equations-by-12rytcavkb.pdf

Solving System of Fractional Differential Equations by Fractional Complex Transform Method

In this paper, the modification of the homotopy perturbation method (MHPM) Zaid M. Odibat (Appl. Math. Comput. 2007 ) is extended to derive approximate solutions of the nonlinear coupled wave equations. This work will present a numerical comparison between the modification and the homotopy perturbation method (HPM). In order to show the ability and reliability of the method some examples are provided. The results reveal that the method is very effective and simple. The modified method accelerates the rapid convergence of the series solution and reduces the size of work.

/pdf/modification-of-the-homotopy-perturbation-method-for-azehiy823h.pdf

Bahman Ghazanfari

Papers

Numerical solutions of fuzzy differential equations by extended Runge--Kutta-like formulae of order 4

Adomian Decomposition Method for Solving Fractional Bratu-type Equations

Homotopy analysis method for the fractional nonlinear equations

Solving System of Fractional Differential Equations by Fractional Complex Transform Method

Modification of the Homotopy Perturbation Method for Numerical Solution of Nonlinear Wave and System of Nonlinear Wave Equations