Exact analytical solutions of the fractional biological population model, fractional EW and modified EW equations

Abstract

In this paper, exact analytical solutions of the biological population model, the EW and the modified EW equations with a conformable derivative operator have been examined by means of the trial solution algorithm and the complete discrimination system. Dark, bright and singular traveling wave solutions of the equations have been obtained by algorithm. Also, revealed singular periodic solutions have been listed. All solutions were verified by substituting them into their corresponding equation via Mathematica package program.

Synchronization of Incommensurate Fractional-order King Cobra Chaotic System

“…Fractional-order analysis offers new perspectives for observing, modeling, and controlling the nature around us [1]. For this reason, many systems in fields such as physics [2], engineering [3], mathematical biology [4], health [5], computer science [6], and more can be described with the help of fractional derivatives.…”

Partial Stability of Conformable Stochastic Systems

“…In the last decades, it has established its effectiveness as an essential tool in many real-world applications, such as physics [7], biology [4,8,9], and control theory [2,3,5,[10][11][12][13][14]. In fact, Neirameh in [4] proposed a new method to find exact solutions of the general biological population model.…”

“…In fact, Neirameh in [4] proposed a new method to find exact solutions of the general biological population model. By using the trial solution algorithm and the complete discrimination system, Odabasi in [9] has proved the existence of the exact solutions of the biological population model. Using the fixed-point method, Das in [2] showed the controllability and the existence of mild solution for a class of nonlinear systems.…”

Stability of conformable stochastic systems depending on a parameter

“…In particular, the stability theory of the solution of conformable fractional-order nonlinear deterministic and stochastic systems has attracted much more attention (see [6], [7], [8], and [9]). Recently, it has established its effectiveness as an important tools in many fields applications, such as control theory [6,7,[9][10][11][12][13][14][15], physics [16], or biology [8,17,18]. In fact, Neirameh in [8] suggested a method to find exact solitary wave solutions of extended biological population model.…”

“…In fact, Neirameh in [8] suggested a method to find exact solitary wave solutions of extended biological population model. By using the complete discrimination system and the trial solution algorithm, Odabasi in [18] has examined the exact analytical solutions of the biological population model. Using the Banach-fixed point theorem Das in [6] established the controllability for a class of nonlinear systems.…”