Derivative (finance)

Physics

Korteweg–de Vries equation

Nonlinear system

Operator (biology)

Riemann hypothesis

Mathematics

Transcription factor

Gene

Financial economics

Fractional calculus

Mathematical analysis

Repressor

Economics

Variable (mathematics)

Chemistry

Programming language

Computer science

Quantum mechanics

Applied mathematics

Integer (computer science)

Biochemistry

Alexandria Engineering Journal

The main goal of this paper is to discover some new analytical solutions of a fractional form of the Bogoyavlensky–Konopelchenko equation via two new analytical schemes. This model is considered as a particular case of (2 + 1)–dimensional version of the well–known KdV equation where it describes the interaction between the Riemann wave propagating and the long-wave propagation along the x,y–axises. An efficient fractional derivative called Atangana–Baleanu-Riemann derivative is utilized to convert the standard form of the model into a nonlinear fractional PDE with an–integer order. The basic idea in these methods is to use a new variable to transform the form of the equation into a nonlinear equation with ordinary derivatives. The novelty of the present paper is that the new solutions determined by applying these two powerful analytical methods can not be found in previous articles. Several two and three-dimensional figures have been depicted to illustrate the dynamic behavior of the acquired solutions. Another advantage of these two methods is their applicability in solving similar models using this fractional derivative operator.

Novel exact solutions of the fractional Bogoyavlensky–Konopelchenko equation involving the Atangana-Baleanu-Riemann derivative