New exact solutions for some fractional order differential equations via improved sub-equation method

Berat Karaagac

doi:10.3934/dcdss.2019029

Article Contents

2019, Volume 12, Issue 3: 447-454. Doi: 10.3934/dcdss.2019029

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New exact solutions for some fractional order differential equations via improved sub-equation method

Berat Karaagac

Department of Mathematic Education, Adıyaman University, Adıyaman, Turkey

Received: May 31, 2017

Published: October 2018

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Abstract

In this paper, improved sub-equation method is proposed to obtain new exact analytical solutions for some nonlinear fractional differential equations by means of modified Riemann Liouville derivative. The method is applied to time-fractional biological population model and space-time fractional Fisher equation successfully. Finally, simulations of new exact analytical solutions are presented graphically.

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Mathematics Subject Classification: 83C15, 34A08.

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Figure 1. The numerical simulations of real and imaginal part for fractional Biological Population Model for $u^{3}_{1}$, respectively

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Figure 2. The numerical simulations of fractional Fisher equation for $u^{1}_{1}$, $u^{1}_{2}$, $u^{3}_{1}$ and $u^{4}_{1}$, respectively

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