Santanu Raut

Bio: Santanu Raut is an academic researcher. The author has contributed to research in topics: Allee effect & Burgers' equation. The author has an hindex of 1, co-authored 3 publications receiving 1 citations.

Solution of space time fractional generalized KdV equation, KdV burger equation and Bona-Mahoney-Burgers equation with dual power-law nonlinearity using complex fractional transformation

Abstract: Fractional calculus is a rising subject in the current research field. The researchers of different disciplines are using fractional calculus models to investigate different practical problems. In this paper, we found the exact solutions of space-time fractional generalized KdV equation, KdV Burger equation and Benjamin-Bona-Mahoney-Burgers equation with dual power-law nonlinearity. The solutions are expressed in terms of hyperbolic, trigonometric and rational functions.

D Alemberts solution of fractional wave equations using complex fractional transformation

Abstract: Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation is difficult to find. Usually Laplace-Fourier transformation method, along with methods where solutions are represented in series form is used to find the solution of the fractional wave equation. In this paper we describe the D Alembert s solution of the fractional wave equation with the help of complex fractional transform method. We demonstrate that using this fractional complex transformation method, we obtain the solutions easily as compared to fractional method of characteristics; and get the solution in analytical form. We show that the solution to the fractional wave equation manifests as travelling waves with scaled coordinates, depending on the considered fractional order value.

Approximate Analytical Solutions of Generalized Zakharov–Kuznetsov and Generalized Modified Zakharov–Kuznetsov Equations

Abstract: This paper investigates the generalized Zakharov–Kuznetsov (GZK) equation and generalized modified Zakharov–Kuznetsov equation in the presence of external periodic forcing term together with damping. An approximate analytical solution is obtained by employing the direct assumption technique. The framework staged here reveals number of beautiful wave features such as positive amplitude soliton, rare effective soliton, periodic rational soliton, kink type soliton, etc. Moreover, two new parameters along with a control function is introduced to extend the study of traveling wave solution and to create new types of solitary wave solution that are depicted from a numerical standpoint. It is noticed that the generalized wave solution for GZK in presence of external periodic forcing with a damping, positive potential soliton may transform into a rare effective soliton due to an increase in the nonlinearity of the system.

Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect

Abstract: In an ecological system, omnivores are often significantly important as they feed upon more than one trophic level in a food chain model. Intraguild predation is a special kind of omnivory that is ubiquitous in many ecological communities. A lot of field experiments suggest that the experience over a time duration in the recent past affects the growth rate of all species at the present time. Here, we have considered the Caputo type fractional ordered three-species food chain model. The memory effect is explained in terms of the order of the fractional derivative. Intermediate, top predators feed upon prey by Holling type I functional response and the top predator consumes intermediate predator by Holling type II functional response. Here, we established the existence and uniqueness of the solution of the considered system. Also, we prove the positivity and boundedness of the system solution. All possible feasible equilibrium points with required parametric conditions are discussed in the text. The local stability of all feasible equilibrium points and the parametric conditions of global stability of all non-trivial equilibrium points are discussed. The memory effect can stabilize the system from the periodic oscillatory situation which has been proved through the Hopf bifurcation analysis. Finally, some numerical simulation has been carried out to make significant comments on the dynamics of the considered system about the memory effect and other system parameters. It is clear from the numerical simulations that the order of fractional derivative can be taken as the indicator of chaos control. The biological interpretations make the article most significant from the ecological point of view.

A Fractional-Order Predator-Prey Model with Age Structure on Predator and Nonlinear Harvesting on Prey

Abstract: In this manuscript, the dynamics of a fractional-order predator-prey model with age structure on predator and nonlinear harvesting on prey are studied. The Caputo fractional-order derivative is used as the operator of the model by considering its capability to explain the present state as the impact of all of the previous conditions. Three biological equilibrium points are successfully identified including their existing properties. The local dynamical behaviors around each equilibrium point are investigated by utilizing the Matignon condition along with the linearization process. The numerical simulations are demonstrated not only to show the local stability which confirms all of the previous analytical results but also to show the existence of periodic signal as the impact of the occurrence of Hopf bifurcation.