New exact solution of generalized biological population model

Volume 10, Issue 7, pp 3916--3929 http://dx.doi.org/10.22436/jnsa.010.07.44

Publication Date: July 27, 2017 Submission Date: May 05, 2017

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Authors

Omer Acan - Art and Science Faculty, Department of Mathematics, Siirt University, Siirt, Turkey. Maysaa Mohamed Al Qurashi - Faculty of Art and Science, Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia. Dumitru Baleanu - Faculty of Art and Science, Department of Mathematics, Cankaya University, Ankara, Turkey. - Institute of Space Sciences, Magurele-Bucharest, Romania.

Abstract

In this study, a mathematical model of the generalized biological population model (GBPM) gets a new exact solution with a conformable derivative operator (CDO). The new exact solution of this model will be obtained by a new approximate analytic technique named three dimensional conformable reduced differential transform method (TCRDTM). By using this technique, it is possible to find new exact solution as well as closed analytical approximate solution of a partial differential equations (PDEs). Three numerical applications of GBPM are given to check the accuracy, effectiveness, and convergence of the TCRDTM. In these applications, obtained new exact solutions in conformable sense are compared with the exact solutions in Caputo sense in literature. The comparisons are illustrated in 3D graphics. The results show that when \(\alpha\rightarrow 1\), the exact solutions in conformable and Caputo sense converge to each other. In other cases, exact solutions different from each other are obtained.

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Keywords

• Numerical solution
• biological populations model
• reduced differential transform method
• conformable derivative
• partial differential equations.

MSC

•  35R11
•  74H15

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