A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model

A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model

In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge–Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel met...

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Main Authors: Muhammad Sarmad Arshad, Dumitru Baleanu, Muhammad Bilal Riaz, Muhammad Abbas
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/1020472
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spelling doaj-5ed107806050422fa733aad63e4275162020-11-25T03:20:57ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/10204721020472A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth ModelMuhammad Sarmad Arshad0Dumitru Baleanu1Muhammad Bilal Riaz2Muhammad Abbas3Department of Mathematics, Lahore Garrison University, Lahore, PakistanDepartment of Mathematics, Çankaya University, Ankara, TurkeyDepartment of Mathematics, University of Management and Technology, Lahore, PakistanDepartment of Mathematics, University of Sargodha, Sargodha, PakistanIn this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge–Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge–Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.http://dx.doi.org/10.1155/2020/1020472
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Sarmad Arshad
Dumitru Baleanu
Muhammad Bilal Riaz
Muhammad Abbas
spellingShingle Muhammad Sarmad Arshad
Dumitru Baleanu
Muhammad Bilal Riaz
Muhammad Abbas
A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model
Discrete Dynamics in Nature and Society
author_facet Muhammad Sarmad Arshad
Dumitru Baleanu
Muhammad Bilal Riaz
Muhammad Abbas
author_sort Muhammad Sarmad Arshad
title A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model
title_short A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model
title_full A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model
title_fullStr A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model
title_full_unstemmed A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model
title_sort novel 2-stage fractional runge–kutta method for a time-fractional logistic growth model
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2020-01-01
description In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge–Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge–Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.
url http://dx.doi.org/10.1155/2020/1020472
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