On numerical solution to fractional non-linear oscillatory equations
TLDR
In this paper, the multi-step differential transform method (MsDTM) is applied to give approximate solutions of nonlinear ordinary differential equation such as fractional-non-linear oscillatory and vibration equations.Abstract:
In this article, the multi-step differential transform method (MsDTM) is applied to give approximate solutions of nonlinear ordinary differential equation such as fractional-non-linear oscillatory and vibration equations The results indicate that the method is very effective and sufficient for solving nonlinear differential equations of fractional orderread more
Citations
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Generalized differential transform method for nonlinear boundary value problem of fractional order
TL;DR: The generalized differential transform method is applied to obtain an approximate solution of linear and nonlinear differential equation of fractional order with boundary conditions and results show that the method is effective, easier to implement and very accurate when applied for the solution of fractionsal boundary values problems.
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Vibrations of an elastic rod on a viscoelastic foundation of complex fractional Kelvin–Voigt type
TL;DR: In this paper, the authors considered vibrations of an elastic rod loaded by axial force of constant intensity and positioned on a viscoelastic foundation of complex order fractional derivative type.
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A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations
TL;DR: A more efficient and accurate tool is found to inspect the solution of fractional-order highly nonlinear models as a result of the proposed Picard Chelyshkov polynomial method and Picard iterative scheme.
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A robust scheme based on novel‐operational matrices for some classes of time‐fractional nonlinear problems arising in mechanics and mathematical physics
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Noether symmetries for fractional generalized Birkhoffian systems in terms of classical and combined Caputo derivatives
Ying Zhou,Yi Zhang +1 more
TL;DR: In this paper, the generalized Pfaff-Birkhoff principle and Birkhoff's equations with classical and combined Caputo derivatives are given, and two kinds of Noether symmetry and their conserved quantities by the method of time re-parameterization.
References
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Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
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Solution of fractional differential equations by using differential transform method
Aytac Arikoglu,Ibrahim Ozkol +1 more
TL;DR: In this article, the authors implemented a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations and the results obtained are in good agreement with the existing ones in open literature.
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Solutions of the system of differential equations by differential transform method
TL;DR: Three-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time and exact solutions of linear and non-linear systems of partial differential equations have been investigated.
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A generalized differential transform method for linear partial differential equations of fractional order
Zaid Odibat,Shaher Momani +1 more
TL;DR: A new generalization of the two-dimensional differential transform method is developed that will extend the application of the method to linear partial differential equations with space- and time-fractional derivatives, generalized Taylor’s formula and Caputo fractional derivative.
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Analytical approach to linear fractional partial differential equations arising in fluid mechanics
Shaher Momani,Zaid Odibat +1 more
TL;DR: In this article, the variational iteration method and the Adomian decomposition method are used for solving linear fractional partial differential equations arising in fluid mechanics, where the solution takes the form of a convergent series with easily computable components.