New exact solution of generalized biological population model

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 α → 1, the exact solutions in conformable and Caputo sense converge to each other. In other cases, exact solutions different from each other are obtained.

Cobweb model with conformable fractional derivatives

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Some exact solutions of a variable coefficients fractional biological population model

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Asymptotical stability analysis of conformable fractional systems

“…Fractional differential systems have gained considerable popularity due to its important applications in physics and engineering [1][2][3][4][5][6][7][8] etc. In recent years, several types of fractional definitions are given, such as Riemann-Liouville, Grunwald-Letnikov and Caputo's fractional definition and so on.…”