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Generalized fractional power series solutions for fractional differential equations

Applied Mathematics Letters, 2020
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Christopher N Angstmann, B I Henry
exaly   +5 more sources

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Residual Power Series Method for Fractional Diffusion Equations

Fundamenta Informaticae, 2017
In this article, improved residual power series method (RPSM) is effectively implemented to find the approximate analytical solution of a time fractional diffusion equations. The proposed method is an analytic technique based on the generalized Taylor’s series formula which construct an analytical solution in the form of a convergent series.
Amit Kumar, Sunil Kumar, Sheng-Ping Yan
openaire   +1 more source

Representation of Algebraic Functions As Power and Fractional Power Series of Special Type

Programming and Computer Software, 2001
Let \(K\) be a field and let \(f\in K[x,y]\). The equation \(f(x,y)= 0\) defines a function \(y(x)\) which expands to a fractional power series, or Puiseux series, \[ y(x)= \sum^\infty_{n= n_0} \alpha_n(x- x_0)^{n/\varepsilon},\tag{1} \] where \(\varepsilon\in \mathbb{N}\), \(n_0\in\mathbb{Z}\).
A. M. Mitichkina, Anna A. Ryabenko
openaire   +2 more sources

ON FORMAL CONTINUED FRACTIONS RELATED TO POWER SERIES EXPANSION

JP Journal of Algebra, Number Theory and Applications, 2018
Summary: We obtain formal continued fraction of a large class of functions using their power series expansion and symbolic computation.
Chammam, Wathek, Alhussain, Ziyad A.
openaire   +1 more source

Continued Fractions of Algebraic Power Series in Characteristic 2

The Annals of Mathematics, 1976
Let \(K=\mathbb F_2 ((x^{-1}))\) be the field of formal power series in \(x^{-1}\) over \(F= \mathbb F_2\), the field with two elements. There is a continued fraction theory for \(K\), analogous to that for real numbers, with polynomials in \(x\) playing the role of the integers. The following theorems are shown: Theorem 1.
Baum, Leonard E., Sweet, Melvin M.
openaire   +1 more source

A GENERALIZED FRACTIONAL POWER SERIES FOR SOLVING NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

Far East Journal of Mathematical Sciences (FJMS), 2019
Summary: In this paper, an analytical solution to nonlinear fractional integro-differential equations based on a generalized fractional power series expansion is presented. The fractional derivatives are of the conformable type. The new approach is a modified form of the well-known Taylor series expansion.
Thanompolkrang, Sirunya, Poltem, Duangkamol   +1 more
openaire   +1 more source

Continued fractions of formal power series

1993
Abstract I will discuss continued fractions of formal power series, not for their own sake, but in terms of their use in obtaining explicit continued fraction expansions of classes of numbers. As we will see, the approach I outline accounts for essentially all the interesting examples of the past dozen years.
openaire   +1 more source

Continued Fraction Expansions for Arbitrary Power Series

The Annals of Mathematics, 1940
Scott, W. T., Wall, H. S.
openaire   +2 more sources

Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations

Mathematics, 2021
Pshtiwan Othman Mohammed, J A Tenreiro Machado, Juan L G Guirao   +2 more
exaly  

Application of Laplace residual power series method for approximate solutions of fractional IVP’s

AEJ - Alexandria Engineering Journal, 2022
Mohammad Alaroud
exaly