A novel algorithm for time-fractional foam drainage equation

Qasem M. Al-Mdallal; Haruon Yusuf; Alaa Ali

doi:10.1016/j.aej.2020.04.007

A novel algorithm for time-fractional foam drainage equation

Qasem M. Al-Mdallal
, Haruon Yusuf
, Alaa Ali

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

41 Citations (Scopus)

Abstract

In this work, we present a novel numerical algorithm for solving the nonlinear time-fractional foam drainage equation at early stages of the time. The analytical solution of the nonlinear time-fractional foam drainage equation is represented by a linear combination of fractional Bernstein basis polynomials over a time interval [0,T]. Detailed numerical algorithm with several theoretical results are discussed. Several examples are discussed to test the efficiency and accuracy of the present scheme.

Original language	English
Pages (from-to)	1607-1612
Number of pages	6
Journal	Alexandria Engineering Journal
Volume	59
Issue number	3
DOIs	https://doi.org/10.1016/j.aej.2020.04.007
Publication status	Published - Jun 2020

Keywords

Caputo's fractional derivative
Fractional Bernstein polynomials
Fractional foam drainage equation

ASJC Scopus subject areas

General Engineering

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10.1016/j.aej.2020.04.007

Cite this

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title = "A novel algorithm for time-fractional foam drainage equation",

abstract = "In this work, we present a novel numerical algorithm for solving the nonlinear time-fractional foam drainage equation at early stages of the time. The analytical solution of the nonlinear time-fractional foam drainage equation is represented by a linear combination of fractional Bernstein basis polynomials over a time interval [0,T]. Detailed numerical algorithm with several theoretical results are discussed. Several examples are discussed to test the efficiency and accuracy of the present scheme.",

keywords = "Caputo's fractional derivative, Fractional Bernstein polynomials, Fractional foam drainage equation",

author = "Al-Mdallal, \{Qasem M.\} and Haruon Yusuf and Alaa Ali",

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year = "2020",

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AU - Al-Mdallal, Qasem M.

AU - Yusuf, Haruon

AU - Ali, Alaa

PY - 2020/6

Y1 - 2020/6

N2 - In this work, we present a novel numerical algorithm for solving the nonlinear time-fractional foam drainage equation at early stages of the time. The analytical solution of the nonlinear time-fractional foam drainage equation is represented by a linear combination of fractional Bernstein basis polynomials over a time interval [0,T]. Detailed numerical algorithm with several theoretical results are discussed. Several examples are discussed to test the efficiency and accuracy of the present scheme.

AB - In this work, we present a novel numerical algorithm for solving the nonlinear time-fractional foam drainage equation at early stages of the time. The analytical solution of the nonlinear time-fractional foam drainage equation is represented by a linear combination of fractional Bernstein basis polynomials over a time interval [0,T]. Detailed numerical algorithm with several theoretical results are discussed. Several examples are discussed to test the efficiency and accuracy of the present scheme.

KW - Caputo's fractional derivative

KW - Fractional Bernstein polynomials

KW - Fractional foam drainage equation

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UR - https://www.scopus.com/pages/publications/85085748179#tab=citedBy

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JO - Alexandria Engineering Journal

JF - Alexandria Engineering Journal

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ER -

A novel algorithm for time-fractional foam drainage equation

Abstract

Keywords

ASJC Scopus subject areas

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