Results 1 to 10 of about 251,877 (284)

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   +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

Further studies on ordinary differential equations involving the M-fractional derivative

AIMS Mathematics, 2022
In the current paper, the power series based on the M-fractional derivative is formally introduced. More peciesely, the Taylor and Maclaurin expansions are generalized for fractional-order differentiable functions in accordance with the M-fractional ...
A. Khoshkenar, M. Ilie, K. Hosseini, D. Baleanu , S. Salahshour, C. Park, J. R. Lee   +6 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

Fractional Derivative as Fractional Power of Derivative [PDF]

, 2007
Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator.
Berezin F. A., Berezin F. A., Brichkov Yu. A., Caputo M., Dalechky Yu. L., Hadid S. B., Karasev M. V., Korabel N., Krasnolelsky M. A., Krasnolelsky M. A., Krein S. G., Krein S. G., Le Mehaute A., Luke Y., Maslov V. P., Momani S., Oldham K. B., Samko S. G., Tarasov V. E., Tarasov V. E., Tarasov V. E., Tarasov V. E., Tarasov V. E., Tarasov V. E., VASILY E. TARASOV, Zaslavsky G. M.   +25 more
core   +1 more source

Analytical Solutions of Heat Transfer Model in Two-Dimensional Case of Neutrosophic Fredholm Integro-Di erential Equations [PDF]

Neutrosophic Sets and Systems
This article uses the fractional residual power series (FRPS) method to solve a linear neutrosophic fractional integro-differential equation in two dimensions.
Amer Darweesh, Kamel Al- Khaled, Marwan Alquran, Adel Almalki , Sohad Al-Omari   +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

Analytic solution of homogeneous time-invariant fractional IVP

Advances in Difference Equations, 2018
In this work, we propose a novel analytical solution approach for solving a general homogeneous time-invariant fractional initial value problem in the normal form Dtα[u(x‾,t)]=F(u(x‾,t)),0 ...
Imad Jaradat, Marwan Alquran, Mohammad Al-Dolat   +2 more
doaj   +1 more source