Results 1 to 10 of about 29,735 (296)

New Results on Fractional Power Series: Theory and Applications [PDF]

Entropy, 2013
In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives.
Ahmad El-Ajou, Omar Abu Arqub, Zeyad Al Zhour, Shaher Momani   +3 more
doaj   +4 more sources

Frequency bifurcation in a series-series compensated fractional-order inductive power transfer system

Journal of Advanced Research, 2020
This paper reveals and analyzes the frequency bifurcation phenomena in the fractional-order inductive power transfer (FOIPT) system with series-series compensation topology.
Xujian Shu, Bo Zhang, Chao Rong, Yanwei Jiang   +3 more
doaj   +5 more sources

Some Properties of the Functions Representable as Fractional Power Series

Mathematics
The α-fractional power moduli series are introduced as a generalization of α-fractional power series and the structural properties of these series are investigated.
Ghiocel Groza, Marilena Jianu, Ion Mierluş-Mazilu   +2 more
doaj   +4 more sources

A new iterative algorithm on the time-fractional Fisher equation: Residual power series method

Advances in Mechanical Engineering, 2017
In this article, the residual power series method is used to solve time-fractional Fisher equation. The residual power series method gets Maclaurin expansion of the solution.
Maysaa’ Mohamed Al Qurashi, Zeliha Korpinar, Dumitru Baleanu, Mustafa Inc   +3 more
doaj   +2 more sources

Approximate Analytical Solutions of Time Fractional Whitham–Broer–Kaup Equations by a Residual Power Series Method

Entropy, 2015
In this paper, a new analytic iterative technique, called the residual power series method (RPSM), is applied to time fractional Whitham–Broer–Kaup equations. The explicit approximate traveling solutions are obtained by using this method.
Linjun Wang, Xumei Chen
doaj   +3 more sources

A Vector Series Solution for a Class of Hyperbolic System of Caputo Time-Fractional Partial Differential Equations With Variable Coefficients

Frontiers in Physics, 2021
In this paper, we introduce a series solution to a class of hyperbolic system of time-fractional partial differential equations with variable coefficients. The fractional derivative has been considered by the concept of Caputo.
Ahmad El-Ajou, Zeyad Al-Zhour
doaj   +1 more source

Reliable solutions to fractional Lane-Emden equations via Laplace transform and residual error function

Alexandria Engineering Journal, 2022
In this paper, a reliable analytical solution for a class of the fractional Lane-Emden equations is prepared. A new technique, the Laplace-residual power series, is employed to construct a series solution to the equations.
Rania Saadeh, Aliaa Burqan, Ahmad El-Ajou   +2 more
doaj   +1 more source

Adaptation of Residual-Error Series Algorithm to Handle Fractional System of Partial Differential Equations

Mathematics, 2021
In this article, an attractive numeric–analytic algorithm, called the fractional residual power series algorithm, is implemented for predicting the approximate solutions for a certain class of fractional systems of partial differential equations in terms
Hussam Aljarrah, Mohammad Alaroud, Anuar Ishak, Maslina Darus   +3 more
doaj   +1 more source

A Novel Solution Approach for Time-Fractional Hyperbolic Telegraph Differential Equation with Caputo Time Differentiation

Mathematics, 2023
In the current analysis, a specific efficient and applicable novel solution approach, based on a fractional power series technique and Laplace transform operator, is considered to predict certain accurate approximate solutions (ASs) for a time-fractional
Mohammad Alaroud, Abedel-Karrem Alomari, Nedal Tahat, Shrideh Al-Omari, Anuar Ishak   +4 more
doaj   +1 more source

Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense

Entropy, 2021
Fuzzy differential equations provide a crucial tool for modeling numerous phenomena and uncertainties that potentially arise in various applications across physics, applied sciences and engineering. Reliable and effective analytical methods are necessary
Malik Bataineh, Mohammad Alaroud, Shrideh Al-Omari, Praveen Agarwal   +3 more
doaj   +1 more source