The investigation of dynamical behaviour variation of (2+1)-dimensional Extended Calogero-Bogoyavlenskii-Schiff Equation with different fractional operators

Abstract

The majority of scientific fields employ differential equations involving fractional-order derivatives to understanda wide range of physical events. Fractional derivatives and integrals have the ability to cop with complicatedproblems. Various types of fractional-order derivative have been dicovered, like -fractional and M-truncatedderivative. In this article the Extended Calogero-Bogoyavlenskii-Schiff Equation (CBSE) is used in its fractionalform to extract the soliton solutions, as well as to observe the behaviour of -fractional and M-truncated derivative.CBSE equation has been used to analyse various events in many fields of research. The analytical solutionsare drawn by using the Jacobi elliptic function (JEF) and the expanded tanh-coth techniques. These analyticalsolutions exhibit solitary and periodic wave behaviours. The perposed techniques are one of the effective methodsto obtain soliton solutions of partial differential equations (PDEs). The results are depicted graphically usingdifferent parametric values and the fractional parameters. The wave behaviour is observed, and shown by 3D and 2D plots.